Optical fiber-to-chip interconnection

ABSTRACT

An apparatus includes a fiber-optic connector configured to be connected between one or more optical fibers having a plurality of fiber cores and a photonic integrated circuit including a plurality of vertical-coupling elements disposed along a main surface of the photonic integrated circuit. The fiber-optic connector includes a polarization beam splitter and a patterned birefringent plate. The polarization beam splitter is configured to split an incident light beam from a corresponding fiber core into a first beam having a first polarization and a second beam having a second polarization different from the first polarization. The patterned birefringent plate includes a first region and a second region, the first region has a first optical birefringence, the second region has a second optical birefringence that is different from the first optical birefringence. The difference in the first and second optical birefringence is caused by performing at least one of (i) applying localized heating to the first region without applying localized heating to the second region to cause the first region to have a lower birefringence as compared to the second region, or (ii) applying different amounts of localized heating to the first and second regions to cause the first region to have a first birefringence and the second region to have a second birefringence different from the first birefringence.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. provisional patent application63/159,768, filed on Mar. 11, 2021, U.S. provisional patent application63/225,779, filed on Jul. 26, 2021, U.S. provisional patent application63/173,253, filed on Apr. 9, 2021, U.S. provisional patent application63/175,021, filed on Apr. 14, 2021, U.S. provisional patent application63/178,501, filed on Apr. 22, 2021, U.S. provisional patent application63/192,852, filed on May 25, 2021, U.S. provisional patent application63/208,759, filed on Jun. 9, 2021, U.S. provisional patent application63/210,437, filed on Jun. 14, 2021, U.S. provisional application63/212,013, filed on Jun. 17, 2021, U.S. provisional patent application63/223,685, filed on Jul. 20, 2021, U.S. provisional patent application63/245,005, filed on Sep. 16, 2021, U.S. provisional patent application63/245,011, filed on Sep. 16, 2021, U.S. provisional patent application63/272,025, filed on Oct. 26, 2021, and U.S. provisional patentapplication 63/316,551, filed on Mar. 4, 2022. The entire contents ofthe above applications are incorporated by reference.

BACKGROUND Field

Various example embodiments relate to optical communication equipmentand, more specifically but not exclusively, to methods and apparatus forinterconnecting arrays of optical fibers with planar photonic integratedcircuits.

Description of the Related Art

This section introduces aspects that may help facilitate a betterunderstanding of the disclosure. Accordingly, the statements of thissection are to be read in this light and are not to be understood asadmissions about what is in the prior art or what is not in the priorart.

As the input/output (I/O) capacities of electronic processing chipsincrease, electrical signals may not provide sufficient I/O capacityacross the limited size of a practically viable electronic chip package.A feasible alternative may be to interconnect electronic chip packagesusing optical signals, which can typically be delivered with a muchhigher I/O capacity per unit area compared to electrical I/Os.

SUMMARY OF THE INVENTION

Disclosed herein are various embodiments of an optical system thatincludes one or more circular-polarization-maintaining fibers foroptically coupling two or more optical or optoelectronic devices. In ageneral aspect, an apparatus includes: a laser configured to providelinearly polarized optical power supply light; and a quarter-wave plateto convert the linearly polarized optical power supply light tocircularly polarized optical power supply light. The apparatus includesa circular-polarization-maintaining fiber configured to propagate thecircularly polarized optical power supply light from the quarter-waveplate; and a polarization beam splitter configured to split thecircularly polarized optical power supply light to generate first powersupply light having a first polarization and second power supply lighthaving a second polarization. The apparatus includes a firstlinear-polarization-maintaining fiber optically coupled to a first portof the polarization beam splitter to receive the first power supplylight; and a second linear-polarization-maintaining fiber opticallycoupled to a second port of the polarization beam splitter to receivethe second power supply light.

In another general aspect, an apparatus includes: a first laserconfigured to generate first linearly polarized light; and a firstquarter-wave plate configured to convert the first linearly polarizedlight to first circularly polarized light. The apparatus includes afirst circular-polarization-maintaining fiber having a first endoptically coupled to the first quarter-wave plate; and a secondquarter-wave plate optically coupled to a second end of the firstcircular-polarization-maintaining fiber. The firstcircular-polarization-maintaining fiber is configured to transmit thefirst circularly polarized light from the first quarter-wave plate tothe second quarter-wave plate, and the second quarter-wave plate isconfigured to convert the first circularly polarized light to secondlinearly polarized light. The apparatus includes a first opticalmodulator configured to modulate the second linearly polarized light.

Implementations can include one or more of the following features. Theapparatus can include a first photonic integrated circuit includingcircuitry that is configured to generate a first electrical signal. Thefirst optical modulator can be part of the photonic integrated circuit,and the first optical modulator can be configured to modulate the secondlinearly polarized light based on the first electrical signal.

The apparatus can include: a second laser configured to generate thirdlinearly polarized light. The first quarter-wave plate can be configuredto convert the third linearly polarized light to second circularlypolarized light. The apparatus can include a secondcircular-polarization-maintaining fiber having a first end opticallycoupled to the first quarter-wave plate and a second end opticallycoupled to the second quarter-wave plate. The secondcircular-polarization-maintaining fiber can be configured to transmitthe second circularly polarized light from the first quarter-wave plateto the second quarter-wave plate. The second quarter-wave plate can beconfigured to convert the second circularly polarized light to fourthlinearly polarized light. The apparatus can include a second opticalmodulator configured to modulate the fourth linearly polarized light.

The first laser and the second laser can be aligned such that the firstlinearly polarized light has a polarization direction that issubstantially parallel to the polarization direction of the thirdlinearly polarized light.

The apparatus can include a substrate. The first optical modulator andthe second optical modulator can be mounted on the substrate.

The second quarter-wave plate can be at least one of edge-coupled orvertically coupled to the substrate.

In another general aspect, an apparatus includes: a first substrate; anda first laser mounted on the first substrate and configured to generatefirst linearly polarized light. The apparatus includes a firstquarter-wave polarization rotator mounted on the first substrate andconfigured to convert the first linearly polarized light to firstcircularly polarized light. The apparatus includes a firstcircular-polarization-maintaining fiber having a first end opticallycoupled to the first quarter-wave polarization rotator. The apparatusincludes a second substrate and a second quarter-wave polarizationrotator mounted on the second substrate and optically coupled to asecond end of the first circular-polarization-maintaining fiber. Thefirst circular-polarization-maintaining fiber is configured to transmitthe first circularly polarized light from the first quarter-wavepolarization rotator to the second quarter-wave polarization rotator,and the second quarter-wave polarization rotator is configured toconvert the first circularly polarized light to second linearlypolarized light. The apparatus includes a first optical modulatormounted on the second substrate and configured to modulate the secondlinearly polarized light.

Implementations can include one or more of the following features. Thefirst circular-polarization-maintaining fiber can be at least one ofedge-coupled or vertically coupled to the second substrate.

The apparatus can include: a second laser mounted on the first substrateand configured to generate third linearly polarized light; and a thirdquarter-wave polarization rotator mounted on the first substrate andconfigured to convert the third linearly polarized light to secondcircularly polarized light. The apparatus can include a secondcircular-polarization-maintaining fiber having a first end opticallycoupled to the second quarter-wave polarization rotator; and a fourthquarter-wave polarization rotator mounted on the second substrate andoptically coupled to a second end of the secondcircular-polarization-maintaining fiber. The secondcircular-polarization-maintaining fiber can be configured to transmitthe second circularly polarized light from the third quarter-wavepolarization rotator to the fourth quarter-wave polarization rotator.The fourth quarter-wave polarization rotator can be configured toconvert the second circularly polarized light to fourth linearlypolarized light. The apparatus can include a second optical modulatormounted on the second substrate and configured to modulate the fourthpolarized light.

The first laser and the second laser can be aligned such that the firstlinearly polarized light has a polarization direction that issubstantially parallel to the polarization direction of the thirdlinearly polarized light.

In another general aspect, an apparatus includes: a first laserconfigured to generate first linearly polarized light; and a secondlaser configured to generate second linearly polarized light. Theapparatus includes a first polarization beam splitter configured tocombine the first linearly polarized light and the second linearlypolarized light to generate a first linearly polarized combined light;and a first quarter-wave plate or quarter-wave polarization rotatorconfigured to convert the first linearly polarized combined light tofirst circularly polarized combined light. The apparatus includes afirst circular-polarization-maintaining fiber having a first endoptically coupled to the first quarter-wave plate or quarter-wavepolarization rotator; and a second quarter-wave plate or quarter-wavepolarization rotator optically coupled to a second end of the circularpolarization maintaining fiber. The firstcircular-polarization-maintaining fiber is configured to transmit thefirst circularly polarized combined light from the first quarter-waveplate or quarter-wave polarization rotator to the second quarter-waveplate or quarter-wave polarization rotator, and the second quarter-waveplate or quarter-wave polarization rotator is configured to convert thefirst circularly polarized combined light to second linearly polarizedcombined light. The apparatus includes a second polarization beamsplitter configured to separate the second linearly polarized combinedlight to a third linearly polarized light and a fourth linearlypolarized light. The apparatus includes a first optical modulatorconfigured to modulate the third linearly polarized light; and a secondoptical modulator configured to modulate the fourth linearly polarizedlight.

Implementations can include one or more of the following features. Thefirst linearly polarized light can have a first polarization direction,and the second linearly polarized light can have a second polarizationdirection that is substantially orthogonal to the first polarizationdirection.

The third linearly polarized light can have a third polarizationdirection, and the fourth linearly polarized light can have a fourthpolarization direction that is substantially orthogonal to the thirdpolarization direction.

The first circularly polarized combined light can have a right-handedcircularly polarized component and a left-handed circularly polarizedcomponent.

In another general aspect, an apparatus includes: a photon sourceincludes a first laser source and a second laser source. The photonsource is configured to generate first circularly polarized combinedlight based on light generated by the first laser source and the secondlaser source. The first circularly polarized combined light has aright-handed circularly polarized component and a left-handed circularlypolarized component. The apparatus includes a firstcircular-polarization-maintaining fiber configured to receive the firstcircularly polarized combined light from the photon source. Theapparatus includes a modulator module including a first modulator and asecond modulator. The modulator module is configured to convert thefirst circularly polarized combined light to third linearly polarizedlight and fourth linearly polarized light, the first modulator isconfigured to modulate the third linearly polarized light, and thesecond modulator is configured to modulate the fourth linearly polarizedlight.

Implementations can include one or more of the following features. Thephoton source can include a first polarization beam splitter configuredto combine light generated by the first laser source and light generatedby the second laser source.

The first laser source can be configured to generate first linearlypolarized light, and the second laser source can be configured togenerate second linearly polarized light having a polarization directionthat is substantially orthogonal to the polarization direction of thefirst linearly polarized light.

The second laser source can include a second laser and a polarizationrotator. The second laser can be configured to generate linearlypolarized light having a polarization direction that is substantiallyparallel to the polarization direction of the first linearly polarizedlight, and the polarization rotator can be configured to rotate thepolarization direction of the light from the second laser to cause thesecond linearly polarized light to have the polarization direction thatis substantially orthogonal to the polarization direction of the firstlinearly polarized light.

The photon source can include a first quarter-wave plate configured toreceive light from the polarization beam splitter. The first lasersource can be configured to generate first linearly polarized light, andthe second laser source can be configured to generate second linearlypolarized light having a polarization direction substantially orthogonalto the polarization direction of the first linearly polarized light. Thefirst polarization beam splitter can be configured to combine the firstlinearly polarized light and the second linearly polarized light togenerate first linearly polarized combined light, and the firstquarter-wave plate can be configured to convert the first linearlypolarized combined light to the first circularly polarized combinedlight.

The photon source can include a first quarter-wave plate configured toreceive light from the first laser source and the second laser source.The first laser source can be configured to generate first linearlypolarized light, and the second laser source can be configured togenerate second linearly polarized light having a polarization directionsubstantially orthogonal to the polarization direction of the firstlinearly polarized light. The first quarter-wave plate can be configuredto convert the first linearly polarized light to first circularlypolarized light, and convert the second linearly polarized light tosecond circularly polarized light. The first polarization beam splittercan be configured to combine the first circularly polarized light andthe second circularly polarized light to generate the first circularlypolarized combined light.

The modulator module can include a second polarization beam splitterconfigured to separate the first circularly polarized combined light orlight derived from the first circularly polarized combined light to afirst light component that is provided to the first modulator and asecond light component that is provided to the second modulator.

The modulator module can include a quarter-wave plate configured toreceive the first circularly polarized combined light and generatesecond linearly polarized combined light. The second polarization beamsplitter can be configured to separate the second linearly polarizedcombined light to the third linearly polarized light and the fourthlinearly polarized light.

The modulator module can include a quarter-wave plate configured toreceive light from the second polarization beam splitter. The secondpolarization beam splitter can be configured to separate the firstcircularly polarized combined light to a first circularly polarizedcomponent and a second circularly polarized component. The quarter-waveplate can be configured to convert the first circularly polarizedcomponent to the third linearly polarized light, and convert the secondcircularly polarized component to the fourth linearly polarized light.

The modulator module can include a polarization rotator configured torotate the polarization direction of the light that is provided to oneof the modulators.

In another general aspect, a method includes: at a first light source,generating first circularly polarized light; and transmitting the firstcircularly polarized light through a firstcircular-polarization-maintaining fiber from the first light source to asecond location. The method includes at the second location, convertingthe first circularly polarized light to second linearly polarized light;and modulating the second linearly polarized light.

Implementations can include one or more of the following features.Generating the first circularly polarized light can include generatingfirst linearly polarized light, and converting the first linearlypolarized light to the first circularly polarized light.

Generating the first circularly polarized light can include: generatingfirst linearly polarized light, generating third linearly polarizedlight, combining the first linearly polarized light and the thirdlinearly polarized light to generate first linearly polarized combinedlight, and converting the first linearly polarized combined light to thefirst circularly polarized light. The first circularly polarized lightcan include a first circularly polarized component and a secondcircularly polarized component.

Generating the first circularly polarized light can include: generatingfirst linearly polarized light, generating third linearly polarizedlight, converting the first linearly polarized light to secondcircularly polarized light, converting the third linearly polarizedlight to third circularly polarized light, and combining the secondcircularly polarized light and the third circularly polarized light togenerate the first circularly polarized combined light.

Converting the first circularly polarized light to second linearlypolarized light can include converting the first circularly polarizedlight to third linearly polarized light, and separating the thirdlinearly polarized light to fourth linearly polarized light and fifthlinearly polarized light. Modulating the second linearly polarized lightcan include modulating the fourth linearly polarized light andmodulating the fifth linearly polarized light.

Converting the first circularly polarized light to second linearlypolarized light can include separating the first circularly polarizedlight to a first circularly polarized component and a second circularlypolarized component, converting the first circularly polarized componentto third linearly polarized light, can converting the second circularlypolarized component to fourth linearly polarized light. Modulating thesecond linearly polarized light can include modulating the thirdlinearly polarized light and modulating the fourth linearly polarizedlight.

In another general aspect, a method includes: using a first singlequarter-wave plate to convert a first plurality of linearly polarizedlight to a plurality of circularly polarized light; and transmitting theplurality of circularly polarized light through a plurality ofcircular-polarization-maintaining fibers. The method includes convertingthe circularly polarized light received from the plurality ofcircular-polarization-maintaining fibers to a second plurality oflinearly polarized light; and modulating the second plurality oflinearly polarized light.

Implementations can include one or more of the following features.Converting the circularly polarized light received from the plurality ofcircular-polarization-maintaining fibers to the second plurality oflinearly polarized light can include using a second single quarter-waveplate to convert the circularly polarized light received from theplurality of circular-polarization-maintaining fibers to the secondplurality of linearly polarized light.

In another general aspect, a method includes: at a first photonicintegrated circuit, generating a first plurality of linearly polarizedlight, and converting the first plurality of linearly polarized light toa plurality of circularly polarized light. The method includestransmitting the plurality of circularly polarized light through aplurality of circular-polarization-maintaining fibers from the firstphotonic integrated circuit to a second location. The method includes atthe second location, converting the plurality of circularly polarizedlight to a second plurality of linearly polarized light; and modulatingthe second plurality of linearly polarized light.

Implementations can include one or more of the following features.Converting the first plurality of linearly polarized light to theplurality of circularly polarized light can include using a plurality ofpolarization converters to convert the first plurality of linearlypolarized light to the plurality of circularly polarized light.

Converting the plurality of circularly polarized light to the secondplurality of linearly polarized light can include using a plurality ofpolarization converters to convert the plurality of circularly polarizedlight to the second plurality of linearly polarized light.

In another general aspect, an apparatus includes: a light sourceconfigured to generate first linearly polarized light; and a firstquarter-wave plate configured to convert the first linearly polarizedlight to first circularly polarized light. The apparatus includes afirst circular-polarization-maintaining fiber having a first endoptically coupled to the first quarter-wave plate, and a secondquarter-wave plate optically coupled to a second end of the firstcircular-polarization-maintaining fiber. The firstcircular-polarization-maintaining fiber is configured to transmit thefirst circularly polarized light from the first quarter-wave plate tothe second quarter-wave plate, and the second quarter-wave plate isconfigured to convert the first circularly polarized light to secondlinearly polarized light. The apparatus includes a first optical devicethat accepts the second linearly polarized light.

Implementations can include one or more of the following features. Thefirst optical device can include at least one of a lithium niobateoptical modulator, a vertical grating coupler on a photonic integratedcircuit, or a modulator integrated on a photonic integrated circuit.

The light source can include a local oscillator that is configured togenerate a sequence of optical pulses, and the first optical device caninclude a coherent optical receiver.

The light source can include a single-polarization optical transmitterand the first optical device can include a single-polarization opticalreceiver.

The apparatus can include a first photonic integrated circuit includingcircuitry that is configured to generate a first electrical signal. Thefirst optical device can be part of the photonic integrated circuit, andthe first optical device can be configured to process the secondlinearly polarized light based on the first electrical signal.

The apparatus can include: a second light source configured to generatethird linearly polarized light. The first quarter-wave plate can beconfigured to convert the third linearly polarized light to secondcircularly polarized light. The apparatus can include a secondcircular-polarization-maintaining fiber having a first end opticallycoupled to the first quarter-wave plate and a second end opticallycoupled to the second quarter-wave plate. The secondcircular-polarization-maintaining fiber can be configured to transmitthe second circularly polarized light from the first quarter-wave plateto the second quarter-wave plate. The second quarter-wave plate can beconfigured to convert the second circularly polarized light to fourthlinearly polarized light. The apparatus can include a second opticaldevice that accepts the fourth linearly polarized light.

The first light source and the second light source can be aligned suchthat the first linearly polarized light has a polarization directionthat is substantially parallel to the polarization direction of thethird linearly polarized light.

The apparatus can include a substrate. The first optical device and thesecond optical device can be mounted on the substrate.

The second quarter-wave plate can be at least one of edge-coupled orvertically coupled to the substrate.

In another general aspect, an apparatus includes: a first substrate; anda first light source mounted on the first substrate and configured togenerate first linearly polarized light. The apparatus includes a firstquarter-wave polarization rotator mounted on the first substrate andconfigured to convert the first linearly polarized light to firstcircularly polarized light; and a firstcircular-polarization-maintaining fiber having a first end opticallycoupled to the first quarter-wave polarization rotator. The apparatusincludes a second substrate; and a second quarter-wave polarizationrotator mounted on the second substrate and optically coupled to asecond end of the first circular-polarization-maintaining fiber. Thefirst circular-polarization-maintaining fiber is configured to transmitthe first circularly polarized light from the first quarter-wavepolarization rotator to the second quarter-wave polarization rotator,and the second quarter-wave polarization rotator is configured toconvert the first circularly polarized light to second linearlypolarized light. The apparatus includes a first optical device mountedon the second substrate and configured to modulate the second linearlypolarized light.

Implementations can include one or more of the following features. Thefirst circular-polarization-maintaining fiber can be at least one ofedge-coupled or vertically coupled to the second substrate.

The apparatus can include: a second light source mounted on the firstsubstrate and configured to generate third linearly polarized light; anda third quarter-wave polarization rotator mounted on the first substrateand configured to convert the third linearly polarized light to secondcircularly polarized light. The apparatus can include a secondcircular-polarization-maintaining fiber having a first end opticallycoupled to the second quarter-wave polarization rotator; and a fourthquarter-wave polarization rotator mounted on the second substrate andoptically coupled to a second end of the secondcircular-polarization-maintaining fiber. The secondcircular-polarization-maintaining fiber can be configured to transmitthe second circularly polarized light from the third quarter-wavepolarization rotator to the fourth quarter-wave polarization rotator,and the fourth quarter-wave polarization rotator can be configured toconvert the second circularly polarized light to fourth linearlypolarized light. The apparatus can include a second optical modulatormounted on the second substrate and configured to modulate the fourthpolarized light.

The first light source and the second light source can be aligned suchthat the first linearly polarized light has a polarization directionthat is substantially parallel to the polarization direction of thethird linearly polarized light.

In another general aspect, an apparatus includes: a first light sourceconfigured to generate first linearly polarized light; and a secondlight source configured to generate second linearly polarized light. Theapparatus includes a first polarization beam splitter configured tocombine the first linearly polarized light and the second linearlypolarized light to generate a first linearly polarized combined light;and a first quarter-wave plate or quarter-wave polarization rotatorconfigured to convert the first linearly polarized combined light tofirst circularly polarized combined light. The apparatus includes afirst circular-polarization-maintaining fiber having a first endoptically coupled to the first quarter-wave plate or quarter-wavepolarization rotator; and a second quarter-wave plate or quarter-wavepolarization rotator optically coupled to a second end of the circularpolarization maintaining fiber. The firstcircular-polarization-maintaining fiber is configured to transmit thefirst circularly polarized combined light from the first quarter-waveplate or quarter-wave polarization rotator to the second quarter-waveplate or quarter-wave polarization rotator, and the second quarter-waveplate or quarter-wave polarization rotator is configured to convert thefirst circularly polarized combined light to second linearly polarizedcombined light. The apparatus includes a second polarization beamsplitter configured to separate the second linearly polarized combinedlight to a third linearly polarized light and a fourth linearlypolarized light; a first optical device configured to process the thirdlinearly polarized light; and a second optical device configured toprocess the fourth linearly polarized light.

Implementations can include one or more of the following features. Thefirst linearly polarized light can have a first polarization direction,and the second linearly polarized light can have a second polarizationdirection that is substantially orthogonal to the first polarizationdirection.

The third linearly polarized light can have a third polarizationdirection, and the fourth linearly polarized light can have a fourthpolarization direction that is substantially orthogonal to the thirdpolarization direction.

The first circularly polarized combined light can have a right-handedcircularly polarized component and a left-handed circularly polarizedcomponent.

In another general aspect, an apparatus includes: a photon sourceincluding a first light source and a second light source. The photonsource is configured to generate first circularly polarized combinedlight based on light generated by the first light source and the secondlight source, the first circularly polarized combined light has aright-handed circularly polarized component and a left-handed circularlypolarized component. The apparatus includes a firstcircular-polarization-maintaining fiber configured to receive the firstcircularly polarized combined light from the photon source. Theapparatus includes an optical module including a first optical deviceand a second optical device. The optical module is configured to convertthe first circularly polarized combined light to third linearlypolarized light and fourth linearly polarized light, the first opticaldevice is configured to process the third linearly polarized light, andthe second optical device is configured to process the fourth linearlypolarized light.

Implementations can include one or more of the following features. Thephoton source can include a first polarization beam splitter configuredto combine light generated by the first light source and light generatedby the second light source.

The first light source can be configured to generate first linearlypolarized light, and the second light source can be configured togenerate second linearly polarized light having a polarization directionthat is substantially orthogonal to the polarization direction of thefirst linearly polarized light.

The second light source can include a second light generating device anda polarization rotator, and the second light generating device can beconfigured to generate linearly polarized light having a polarizationdirection that is substantially parallel to the polarization directionof the first linearly polarized light. The polarization rotator can beconfigured to rotate the polarization direction of the light from thesecond light generating device to cause the second linearly polarizedlight to have the polarization direction that is substantiallyorthogonal to the polarization direction of the first linearly polarizedlight.

The photon source can include a first quarter-wave plate configured toreceive light from the polarization beam splitter. The first lightsource can be configured to generate first linearly polarized light, andthe second light source can be configured to generate second linearlypolarized light having a polarization direction substantially orthogonalto the polarization direction of the first linearly polarized light. Thefirst polarization beam splitter can be configured to combine the firstlinearly polarized light and the second linearly polarized light togenerate first linearly polarized combined light. The first quarter-waveplate can be configured to convert the first linearly polarized combinedlight to the first circularly polarized combined light.

The photon source can include a first quarter-wave plate configured toreceive light from the first light source and the second light source.The first light source can be configured to generate first linearlypolarized light, and the second light source can be configured togenerate second linearly polarized light having a polarization directionsubstantially orthogonal to the polarization direction of the firstlinearly polarized light. The first quarter-wave plate can be configuredto convert the first linearly polarized light to first circularlypolarized light, and convert the second linearly polarized light tosecond circularly polarized light. The first polarization beam splittercan be configured to combine the first circularly polarized light andthe second circularly polarized light to generate the first circularlypolarized combined light.

The optical module can include a second polarization beam splitterconfigured to separate the first circularly polarized combined light orlight derived from the first circularly polarized combined light to afirst light component that is provided to the first modulator and asecond light component that is provided to the second optical device.

The optical module can include a quarter-wave plate configured toreceive the first circularly polarized combined light and generatesecond linearly polarized combined light. The second polarization beamsplitter can be configured to separate the second linearly polarizedcombined light to the third linearly polarized light and the fourthlinearly polarized light.

The optical module can include a quarter-wave plate configured toreceive light from the second polarization beam splitter. The secondpolarization beam splitter can be configured to separate the firstcircularly polarized combined light to a first circularly polarizedcomponent and a second circularly polarized component. The quarter-waveplate can be configured to convert the first circularly polarizedcomponent to the third linearly polarized light, and convert the secondcircularly polarized component to the fourth linearly polarized light.

The optical module can include a polarization rotator configured torotate the polarization direction of the light that is provided to oneof the optical devices.

In another general aspect, a method includes: at a first light source,generating first circularly polarized light; and transmitting the firstcircularly polarized light through a firstcircular-polarization-maintaining fiber from the first light source to asecond location. The method includes at the second location, convertingthe first circularly polarized light to second linearly polarized light;and processing the second linearly polarized light.

Implementations can include one or more of the following features.Generating the first circularly polarized light can include generatingfirst linearly polarized light, and converting the first linearlypolarized light to the first circularly polarized light.

Generating the first circularly polarized light can include: generatingfirst linearly polarized light, generating third linearly polarizedlight, combining the first linearly polarized light and the thirdlinearly polarized light to generate first linearly polarized combinedlight, and converting the first linearly polarized combined light to thefirst circularly polarized light. The first circularly polarized lightcan include a first circularly polarized component and a secondcircularly polarized component.

Generating the first circularly polarized light can include: generatingfirst linearly polarized light, generating third linearly polarizedlight, converting the first linearly polarized light to secondcircularly polarized light, converting the third linearly polarizedlight to third circularly polarized light, and combining the secondcircularly polarized light and the third circularly polarized light togenerate the first circularly polarized combined light.

Converting the first circularly polarized light to second linearlypolarized light can include converting the first circularly polarizedlight to third linearly polarized light, and separating the thirdlinearly polarized light to fourth linearly polarized light and fifthlinearly polarized light. Processing the second linearly polarized lightcan include processing the fourth linearly polarized light andprocessing the fifth linearly polarized light.

Converting the first circularly polarized light to second linearlypolarized light can include separating the first circularly polarizedlight to a first circularly polarized component and a second circularlypolarized component, converting the first circularly polarized componentto third linearly polarized light, and converting the second circularlypolarized component to fourth linearly polarized light. Processing thesecond linearly polarized light can include processing the thirdlinearly polarized light and processing the fourth linearly polarizedlight.

In another general aspect, a method includes: using a first singlequarter-wave plate to convert a first plurality of linearly polarizedlight to a plurality of circularly polarized light; and transmitting theplurality of circularly polarized light through a plurality ofcircular-polarization-maintaining fibers. The method includes convertingthe circularly polarized light received from the plurality ofcircular-polarization-maintaining fibers to a second plurality oflinearly polarized light; and processing the second plurality oflinearly polarized light.

Implementations can include one or more of the following features.Converting the circularly polarized light received from the plurality ofcircular-polarization-maintaining fibers to the second plurality oflinearly polarized light can include using a second single quarter-waveplate to convert the circularly polarized light received from theplurality of circular-polarization-maintaining fibers to the secondplurality of linearly polarized light.

In another general aspect, a method includes: at a first photonicintegrated circuit, generating a first plurality of linearly polarizedlight, and converting the first plurality of linearly polarized light toa plurality of circularly polarized light. The method includestransmitting the plurality of circularly polarized light through aplurality of circular-polarization-maintaining fibers from the firstphotonic integrated circuit to a second location. The method includes atthe second location, converting the plurality of circularly polarizedlight to a second plurality of linearly polarized light; and processingthe second plurality of linearly polarized light.

Implementations can include one or more of the following features.Converting the first plurality of linearly polarized light to theplurality of circularly polarized light can include using a plurality ofpolarization converters to convert the first plurality of linearlypolarized light to the plurality of circularly polarized light.

Converting the plurality of circularly polarized light to the secondplurality of linearly polarized light can include using a plurality ofpolarization converters to convert the plurality of circularly polarizedlight to the second plurality of linearly polarized light.

In another general aspect, a data center includes any of the apparatusesdescribed above.

In another general aspect, a method includes operating the data centerdescribed above.

In another general aspect, a method includes operating any of theapparatuses described above.

In another general aspect, a method includes assembling any of theapparatuses described above.

In another general aspect, a method includes processing data using anyof the apparatuses described above.

Also disclosed herein are various embodiments of a connector assemblyfor optically connecting one or more optical fibers and an array ofvertical coupling elements of a photonic integrated circuit (PIC).

In another general aspect, an apparatus includes: a fiber-opticconnector configured to optically couple a plurality of optical fibersto a plurality of vertical coupling elements on a photonic integratedcircuit, in which the fiber-optic connector includes a plurality ofcircularly asymmetric optical lenses configured to direct light towardthe vertical coupling elements at one or more angles of incidencerelative to a direction perpendicular to a main surface of the photonicintegrated circuit.

In another general aspect, an apparatus includes: a fiber-opticconnector configured to optically couple a plurality of optical fibersto a plurality of vertical coupling elements on a photonic integratedcircuit, in which the fiber-optic connector includes a plurality ofcircularly asymmetric optical lenses configured to direct light from theoptical fibers toward the vertical coupling elements. Each of at leastsome of the circularly asymmetric optical lenses is configured to directa light beam towards the corresponding vertical coupling element at anangle of incidence relative to a direction perpendicular to a mainsurface of the photonic integrated circuit, and each of at least some ofthe circularly asymmetric optical lenses is asymmetric with respect toan optical axis that is perpendicular to the main surface of thephotonic integrated circuit.

Implementations of the above apparatuses can include one or more of thefollowing features. The plurality of circularly asymmetric opticallenses can be configured to direct light toward the vertical couplingelements at one or more angles of incidence in a range from 1° to 30°relative to the direction perpendicular to the main surface of thephotonic integrated circuit.

The plurality of optical fibers can be arranged in a two-dimensionalarray.

The two-dimensional array can include at least 2 rows and at least 8columns.

The spacing between two adjacent rows in the two-dimensional array canbe identical to the spacing between two adjacent columns in thetwo-dimensional array.

The fiber-optic connector can include first optical elements configuredto process light from the optical fibers to form light beams that aredirected to the circularly asymmetric optical lenses.

The first optical elements can be configured to collimate light from theoptical fibers to form collimated light beams that are directed to thecircularly asymmetric optical lenses.

Each of at least some of the circularly asymmetric optical lenses canhave a surface profile that is configured to focus the light beam to afirst location on the vertical coupling element, and the circularlyasymmetric optical lens can have an optical axis that passes the firstlocation. The first optical element can be positioned and orientedrelative to the circularly asymmetric optical lens such that the lightbeam has a first axis that is parallel to, and offset at a firstdistance from, the optical axis of the circularly asymmetric opticallens.

At least two circularly asymmetric optical lenses can be spaced apart ata second distance in a range from 1.5 to 4.5 times the first distancebetween the first axis and the optical axis, the second distancerepresents the distance between the optical axes of the lenses, thefirst and second distances being measured along a plane parallel to themain surface of the photonic integrated circuit.

The second distance can be in a range from 2 to 3.5 times the firstdistance.

The second distance can be in a range from 2 to 3 times the firstdistance.

The plurality of circularly asymmetric optical lenses can include anarray of circularly asymmetric optical lenses, and each of at least someof the circularly asymmetric optical lenses can be spaced apart from aneighboring circularly asymmetric optical lens at a second distance in arange from 1.5 to 4.5 times the first distance between the first axisand the optical axis of the circularly asymmetric optical lens.

The second distance can be in a range from 2 to 3.5 times the firstdistance.

The second distance can be in a range from 2 to 3 times the firstdistance.

The first axis and the optical axis can be perpendicular to the mainsurface of the photonic integrated circuit.

Each of at least some of the circularly asymmetric optical lenses andthe corresponding first optical element can be positioned relative tothe vertical coupling element such that the first distance between thefirst axis and the optical axis is in a range from 10% to 150% of thefull width at half maximum of the light beam received at the circularlyasymmetric optical lens.

Each of at least some of the circularly asymmetric optical lenses andthe corresponding first optical element can be positioned relative tothe vertical coupling element such that the first distance between thefirst axis and the optical axis is in a range from 20% to 80% of thefull width at half maximum of the light beam received at the circularlyasymmetric optical lens.

Each of at least some of the circularly asymmetric optical lenses can bepositioned relative to the corresponding first optical element such thatthe portion of the light beam received at the circularly asymmetricoptical lens having an intensity greater than half maximum is entirelyoffset from the optical axis of the circularly asymmetric optical lens.

Each of at least some of the circularly asymmetric optical lenses caninclude a truncated version of a rotationally symmetric optical lens,the optical axis of the circularly asymmetric optical lens can overlapthe optical axis of the rotationally symmetric optical lens, and thecircularly asymmetric optical lens can be asymmetric with respect to theoptical axis.

The circularly asymmetric optical lens can have a dimension that is lessthan 1.5 times the radius of the rotationally symmetric optical lens,the dimension of the circularly asymmetric optical lens and the radiusof the rotationally symmetric optical lens can be measured along a planeparallel to the main surface of the photonic integrated circuit.

The circularly asymmetric optical lens can have a dimension that is lessthan 1.2 times the radius of the rotationally symmetric optical lens.

Each of at least some of the circularly asymmetric optical lenses canhave a footprint that is less than 50% of a footprint of thecorresponding rotationally symmetric optical lens.

Each of at least some of the circularly asymmetric optical lenses canhave a dimension that is less than 1.5 times the diameter of the lightbeam received at the circularly asymmetric optical lens, and thediameter of the light beam can be the full width at half maximum of thelight beam.

Each of at least some of the circularly asymmetric optical lenses canhave a footprint having an area that is less than 2.25 times the area ofthe cross section of the light beam received at the circularlyasymmetric optical lens, and the area of the cross section of the lightbeam can be calculated based on the full width at half maximum of thelight beam.

Each of at least some of the circularly asymmetric optical lenses can beconfigured to receive the entire portion of the light beam that has anintensity at half maximum or more.

The first optical elements (e.g., 4610) can be configured to collimatelight from optical fibers having end facets that are polished at anangle in a range from 1 to 30 degrees relative to a plane that isperpendicular to the optical axes of the optical fibers.

The first optical elements (e.g., 4610) can be configured to collimatelight from optical fibers having end facets that are polished at anangle in a range from 4 to 15 degrees relative to the plane that isperpendicular to the optical axes of the optical fibers.

The first optical elements can be configured to collimate light fromoptical fibers having end facets that are polished at an angle in arange from 6 to 10 degrees relative to the plane that is perpendicularto the optical axes of the optical fibers.

The first optical elements (e.g., 4610) can include a second pluralityof circularly asymmetric optical lenses configured to optically couplethe optical fibers to the first plurality of circularly asymmetricoptical lenses.

The second plurality of circularly asymmetric optical lenses can havesurface profiles that are substantially similar to the first pluralityof circularly asymmetric optical lenses.

The plurality of circularly asymmetric optical lenses can be configuredto direct light toward, or receive light from, the vertical couplingelements at one or more angles of incidence in a range from 4° to 15°relative to the direction perpendicular to the main surface of thephotonic integrated circuit.

The plurality of circularly asymmetric optical lenses can be configuredto direct light toward, or receive light from, the vertical couplingelements at one or more angles of incidence in a range from 5° to 12°relative to the direction perpendicular to the main surface of thephotonic integrated circuit.

The plurality of circularly asymmetric optical lenses can be configuredto direct light toward, or receive light from, the vertical couplingelements at one or more angles of incidence in a range from 6° to 10°relative to the direction perpendicular to the main surface of thephotonic integrated circuit.

The plurality of circularly asymmetric optical lenses can be configuredto direct light toward, or receive light from, the vertical couplingelements at one or more offset angles in a range from 7° to 9° relativeto the direction perpendicular to the main surface of the photonicintegrated circuit.

Each of at least some of the circularly asymmetric optical lenses canhave a circular or oval circumference.

Each of at least some of the circularly asymmetric optical lenses canhave a polygonal circumference.

At least some of the circularly asymmetric optical lenses can have asame shape.

The plurality of circularly asymmetric optical lenses can include anarray of rows and columns of circularly asymmetric optical lenses.

The apparatus can include the photonic integrated circuit.

The apparatus can include a first connector element configured to bemechanically and optically coupled to a second connector element that isoptically coupled to the plurality of optical fibers.

The vertical coupling elements can include vertical grating couplers.

The plurality of circularly asymmetric optical lenses can includesilicon lenses.

The photonic integrated circuit can include optical waveguides that arecoupled to the vertical coupling elements.

The fiber-optic connector can include one or more walk-off elementsconfigured to receive input optical beams from one or more of the fibercores, and separate each of at least some of the input optical beamsinto a first optical beam component having a first polarization and asecond optical beam component having a second polarization. Thefiber-optic connector can include a birefringent plate having holes, inwhich the birefringent plate is positioned relative to the one or morewalk-off elements such that each of at least some of the holes isaligned with a corresponding first optical beam component, and thebirefringent plate rotates a polarization of each of at least some ofthe of the second optical beam components to cause the second opticalbeam component to have a same polarization as the corresponding firstoptical beam component.

The plurality of circularly asymmetric optical lenses can include aplurality of pairs of circularly asymmetric optical lenses, and each ofat least some of the pairs of circularly asymmetric optical lenses canbe configured to couple corresponding first and second optical beamcomponents to a pair of vertical coupling elements.

The holes can include at least one of circular holes, square holes,rectangular holes, or strip holes.

A distance between two adjacent optical fibers can be in a range from225 μm to 275 μm, and a distance between two adjacent circularlyasymmetric optical lenses can be in a range from 100√{square root over(2)} μm to 150√{square root over (2)} μm.

In another general aspect, an apparatus includes: a fiber-opticconnector configured to optically couple a plurality of optical fibersto a plurality of vertical coupling elements on a photonic integratedcircuit, in which the fiber-optic connector includes a plurality offree-form off-axis lenses configured to direct light toward the verticalcoupling elements at one or more angles of incidence relative to adirection perpendicular to a main surface of the photonic integratedcircuit.

Implementations can include one or more of the following features. Theplurality of free-form off-axis lenses can be configured to direct lighttoward the vertical coupling elements at one or more angles of incidencein a range from 1° to 30° relative to the direction perpendicular to themain surface of the photonic integrated circuit.

The plurality of optical fibers can be arranged in a two-dimensionalarray.

The two-dimensional array can include at least 2 rows and at least 8columns.

The spacing between two adjacent rows in the two-dimensional array canbe identical to the spacing between two adjacent columns in thetwo-dimensional array.

The fiber-optic connector can include first optical elements configuredto process light from the optical fibers to form light beams that aredirected to the free-form off-axis lenses.

The first optical elements can be configured to collimate light from theoptical fibers to form collimated light beams that are directed to thefree-form off-axis lenses.

Each of at least some of the free-form off-axis lenses can have asurface profile that is configured to focus the light beam to a firstlocation on the vertical coupling element, and the free-form off-axislens can have an optical axis that passes the first location. The firstoptical element can be positioned and oriented relative to the free-formoff-axis lens such that the light beam has a first axis that is parallelto, and offset at a first distance from, the optical axis of thefree-form off-axis lens.

In another general aspect, an apparatus includes: a fiber-opticconnector configured to optically couple a plurality of optical fibersto a plurality of vertical coupling elements on a photonic integratedcircuit. The fiber-optic connector includes: a plurality of first lensesconfigured to collimate light received from the optical fibers togenerate collimated light beams, each of at least some of the firstlenses having an optical axis. The fiber-optic connector includes: aplurality of free-form lenses configured to direct the collimated lightbeams from the plurality of first lenses toward the vertical couplingelements at one or more angles of incidence relative to a directionperpendicular to a main surface of the photonic integrated circuit. Eachfree-form lens has an optical axis, each of at least some of thefree-form lenses is asymmetric with respect to its optical axis, andeach of at least some of the free-form lenses has a focal point on itsoptical axis. Each of at least some of the free-form lenses isconfigured to receive light from a corresponding first lens, the opticalaxis of the free-form lens is parallel to the optical axis of thecorresponding first lens, and the optical axis of the free-form lens isspaced apart at a first distance relative to the optical axis of thefirst lens.

Implementations can include one or more of the following features. Theplurality of free-form lenses can be configured to direct the collimatedlight beams from the plurality of first lenses toward the verticalcoupling elements at one or more angles of incidence in a range from 1°to 30° relative to the direction perpendicular to the main surface ofthe photonic integrated circuit.

The plurality of optical fibers can be arranged in a two-dimensionalarray.

The two-dimensional array can include at least 2 rows and at least 8columns.

The spacing between two adjacent rows in the two-dimensional array canbe identical to the spacing between two adjacent columns in thetwo-dimensional array.

Each of at least some of the free-form off-axis lenses can have asurface profile that is configured to focus the light beam to a firstlocation on the vertical coupling element, and the free-form off-axislens can have an optical axis that passes the first location.

At least two free-form lenses can be spaced apart at a second distancein a range from 1.5 to 4.5 times the first distance between the opticalaxis of the first lens and the optical axis of the free-form lens, inwhich the second distance represents the distance between the opticalaxes of the free-form lenses, and the first and second distances aremeasured along a plane parallel to the main surface of the photonicintegrated circuit.

The second distance can be in a range from 2 to 3.5 times the firstdistance.

The second distance can be in a range from 2 to 3 times the firstdistance.

The plurality of free-form lenses can include an array of circularlyfree-form lenses, and each of at least some of the free-form lenses canbe spaced apart from a neighboring free-form lens at a second distancein a range from 1.5 to 4.5 times the first distance between the opticalaxis of the first lens and the optical axis of the free-form lens.

The second distance can be in a range from 2 to 3.5 times the firstdistance.

The second distance can be in a range from 2 to 3 times the firstdistance.

The first axis and the optical axis can be perpendicular to the mainsurface of the photonic integrated circuit.

Each of at least some of the free-form lenses and the correspondingfirst lens can be positioned relative to the vertical coupling elementsuch that the first distance between the optical axis of the first lensand the optical axis of the free-form lens is in a range from 10% to150% of the full width at half maximum of the light beam received at thefree-form lens.

Each of at least some of the free-form lenses and the correspondingfirst lens can be positioned relative to the vertical coupling elementsuch that the first distance between the optical axis of the first lensand the optical axis of the free-form lens is in a range from 20% to 80%of the full width at half maximum of the light beam received at thefree-form lens.

Each of at least some of the free-form lenses and the correspondingfirst lens can be positioned relative to the vertical coupling elementsuch that the portion of the light beam received at the free-form lenshaving an intensity greater than half maximum is entirely offset fromthe optical axis of the free-form lens.

Each of at least some of the free-form lenses can include a truncatedversion of a rotationally symmetric optical lens, in which the opticalaxis of the free-form optical lens overlaps the optical axis of therotationally symmetric optical lens, and the free-form lens isasymmetric with respect to the optical axis.

The free-form lens can have a dimension that is less than 1.5 times theradius of the rotationally symmetric optical lens, in which thedimension of the free-form lens and the radius of the rotationallysymmetric optical lens are measured along a plane parallel to the mainsurface of the photonic integrated circuit.

The free-form lens can have a dimension that is less than 1.2 times theradius of the rotationally symmetric optical lens.

Each of at least some of the free-form lenses can have a footprint thatis less than 50% of a footprint of the corresponding rotationallysymmetric optical lens.

Each of at least some of the free-form lenses can have a dimension thatis less than 1.5 times the diameter of the light beam received at thefree-form lens, and the diameter of the light beam is the full width athalf maximum of the light beam.

Each of at least some of the free-form lenses can have a footprinthaving an area that is less than 2.25 times the area of the crosssection of the light beam received at the free-form lens, and the areaof the cross section of the light beam is calculated based on the fullwidth at half maximum of the light beam.

The first lenses (e.g., 4610) can be configure to collimate light fromoptical fibers having end facets that are polished at an angle in arange from 1 to 30 degrees relative to a plane that is perpendicular tothe optical axes of the optical fibers.

The first lenses (e.g., 4610) can be configure to collimate light fromoptical fibers having end facets that are polished at an angle in arange from 4 to 15 degrees relative to the plane that is perpendicularto the optical axes of the optical fibers.

The first lenses can be configure to collimate light from optical fibershaving end facets that are polished at an angle in a range from 6 to 10degrees relative to the plane that is perpendicular to the optical axesof the optical fibers.

The first lenses (e.g., 4610) can include a second plurality offree-form lenses configured to optically couple the optical fibers tothe first plurality of free-form lenses.

The second plurality of free-form lenses can have surface profiles thatare substantially similar to the first plurality of free-form lenses.

The first plurality of free-form lenses can be configured to directlight toward, or receive light from, the vertical coupling elements atone or more angles of incidence in a range from 4° to 15° relative tothe direction perpendicular to the main surface of the photonicintegrated circuit.

The first plurality of circularly asymmetric optical lenses can beconfigured to direct light toward, or receive light from, the verticalcoupling elements at one or more angles of incidence in a range from 5°to 12° relative to the direction perpendicular to the main surface ofthe photonic integrated circuit.

The first plurality of free-form lenses can be configured to directlight toward, or receive light from, the vertical coupling elements atone or more angles of incidence in a range from 6° to 10° relative tothe direction perpendicular to the main surface of the photonicintegrated circuit.

The plurality of free-form lenses can be configured to direct lighttoward, or receive light from, the vertical coupling elements at one ormore offset angles in a range from 7° to 9° relative to the directionperpendicular to the main surface of the photonic integrated circuit.

Each of at least some of the free-form lenses can have a circular oroval circumference.

Each of at least some of the free-form lenses can have a polygonalcircumference.

At least some of the free-form lenses can have a same shape.

The plurality of free-form lenses can include an array of rows andcolumns of free-form lenses.

The apparatus can include the photonic integrated circuit.

The apparatus can include a first connector element configured to bemechanically and optically coupled to a second connector element that isoptically coupled to the plurality of optical fibers.

The vertical coupling elements can include vertical grating couplers.

The plurality of free-form lenses can include silicon lenses.

The photonic integrated circuit can include optical waveguides that arecoupled to the vertical coupling elements.

The fiber-optic connector can include one or more walk-off elementsconfigured to receive input optical beams from one or more of the fibercores, and separate each of at least some of the input optical beamsinto a first optical beam component having a first polarization and asecond optical beam component having a second polarization. Thefiber-optic connector can include a birefringent plate having holes, inwhich the birefringent plate is positioned relative to the one or morewalk-off elements such that each of at least some of the holes isaligned with a corresponding first optical beam component, and thebirefringent plate rotates a polarization of each of at least some ofthe of the second optical beam components to cause the second opticalbeam component to have a same polarization as the corresponding firstoptical beam component.

The plurality of first free-form lenses can include a plurality of pairsof free-form lenses, in which each of at least some of the pairs offree-form lenses are configured to couple corresponding first and secondoptical beam components to a pair of vertical coupling elements.

The holes can include at least one of circular holes, square holes,rectangular holes, or strip holes.

A distance between two adjacent optical fibers can be in a range from225 μm to 275 μm, and a distance between two adjacent circularlyasymmetric optical lenses can be in a range from 100√{square root over(2)} μm to 150√{square root over (2)} μm.

In another general aspect, a method includes: transmitting light from aplurality of optical fibers to a plurality of first lenses; anddirecting a plurality of light beams from the plurality of first lensesto a plurality of circularly asymmetric optical lenses. The methodincludes directing, using the circularly asymmetric optical lenses, theplurality of light beams toward a plurality of vertical couplingelements on a photonic integrated circuit at one or more angles ofincidence relative to a direction perpendicular to a main surface of thephotonic integrated circuit.

Implementations can include one or more of the following features.Directing the plurality of light beams toward the plurality of verticalcoupling elements can include directing the plurality of light beamstoward the plurality of vertical coupling elements at one or more anglesof incidence in a range from 10 to 300 relative to the directionperpendicular to the main surface of the photonic integrated circuit.

The plurality of optical fibers can be arranged in a two-dimensionalarray.

The two-dimensional array can include at least 2 rows and at least 8columns.

The spacing between two adjacent rows in the two-dimensional array canbe identical to the spacing between two adjacent columns in thetwo-dimensional array.

Each of at least some of the circularly asymmetric optical lenses caninclude a truncated version of a rotationally symmetric optical lens, inwhich the optical axis of the circularly asymmetric optical lensoverlaps the optical axis of the rotationally symmetric optical lens,and the circularly asymmetric optical lens is asymmetric with respect tothe optical axis.

Transmitting light from a plurality of optical fibers to a plurality offirst lenses can include transmitting light from a plurality of opticalfibers with a 0 degree polish, 0<θ<30° to a second plurality ofcircularly asymmetric lenses.

Transmitting a plurality of light beams from the plurality of firstlenses to a plurality of circularly asymmetric optical lenses caninclude transmitting a plurality of collimated light beams from theplurality of first lenses to the plurality of circularly asymmetricoptical lenses.

In another general aspect, a method includes: transmitting light from aplurality of optical fibers to a plurality of first lenses; anddirecting a plurality of light beams from the plurality of first lensesto a plurality of circularly asymmetric optical lenses. The methodincludes directing, using the plurality of circularly asymmetric opticallenses, the light beams to a plurality of vertical coupling elements ona photonic integrated circuit. Directing the light beams to theplurality of vertical coupling elements on the photonic integratedcircuit includes: directing, using each of at least some of thecircularly asymmetric optical lenses, a light beam towards thecorresponding vertical coupling element at an angle of incidencerelative to a direction perpendicular to a main surface of the photonicintegrated circuit. Each of at least some of the circularly asymmetricoptical lenses is asymmetric with respect to an optical axis that isperpendicular to the main surface of the photonic integrated circuit.

Implementations can include the following feature. Directing the lightbeam towards the corresponding vertical coupling element can includedirecting the light beam towards the corresponding vertical couplingelement at an angle of incidence in a range from 10 to 300 relative tothe direction perpendicular to the main surface of the photonicintegrated circuit.

In another general aspect, a method includes: transmitting light from aplurality of optical fibers to a plurality of first lenses; anddirecting a plurality of light beams from the plurality of first lensesto a plurality of free-form lenses. The method includes directing, usingthe free-form lenses, the plurality of light beams toward a plurality ofvertical coupling elements on a photonic integrated circuit at one ormore angles of incidence relative to a direction perpendicular to a mainsurface of the photonic integrated circuit.

Implementations can include the following feature. Directing theplurality of light beams toward the plurality of vertical couplingelements comprises directing the plurality of light beams toward theplurality of vertical coupling elements at one or more angles ofincidence in a range from 1° to 30° relative to the directionperpendicular to the main surface of the photonic integrated circuit.

In another general aspect, a method includes: transmitting light from atwo-dimensional array of optical fibers to a two-dimensional array offirst lenses, in which each first lens has an optical axis. The methodincludes directing a plurality of collimated light beams from thetwo-dimensional array of first lenses to a two-dimensional array offree-form lenses. The method includes directing, using a two-dimensionalarray of free-form lenses, the collimated light beams from the array offirst lenses toward a two-dimensional array of vertical grating couplerson a photonic integrated circuit at one or more angles of incidencerelative to a direction perpendicular to a main surface of the photonicintegrated circuit. Each free-form lens has an optical axis, each of atleast some of the free-form lenses is asymmetric with respect to itsoptical axis, and each of at least some of the free-form lenses has afocal point on its optical axis. Each of at least some of the free-formlenses receives a collimated light beam from a corresponding first lens,the optical axis of the free-form lens is parallel to the optical axisof the corresponding first lens, and the optical axis of the free-formlens is spaced apart at a first distance relative to the optical axis ofthe first lens.

Implementations can include the following feature. Directing thecollimated light beams from the array of first lenses toward thetwo-dimensional array of vertical grating couplers comprises directingthe collimated light beams from the array of first lenses toward thetwo-dimensional array of vertical grating couplers at one or more anglesof incidence in a range from 1° to 30°

In any of the apparatuses described above, the fiber-optic connector caninclude a second plurality of circularly asymmetric optical lenses thatare not used to direct any light beam towards any vertical couplingelement.

In any of the apparatuses described above, the offset distance betweenthe first axis of the light beam and the optical axis of the circularlyasymmetric optical lens can be at least 10 μm, at least 20 μm, or atleast 40 μm.

In any of the apparatuses described above, the distance between theoptical axis of the first lens and the optical axis of the free-formlens can be at least 10 μm, at least 20 μm, or at least 40 μm.

In another general aspect, a data center includes any of the apparatusesdescribed above.

In another general aspect, a method of operating the data center.

In another general aspect, a method of operating any of the apparatusesdescribed above.

In another general aspect, a method of assembling any of the apparatusesdescribed above.

In another general aspect, a method of processing data using any of theapparatuses described above.

In another general aspect, a method of providing optical power using anyof the apparatuses described above.

In another general aspect, an apparatus includes: one or more opticalfibers having a plurality of fiber cores; a photonic integrated circuitincluding a plurality of vertical-coupling elements disposed along amain surface of the photonic integrated circuit; and a fiber-opticconnector connected between the one or more optical fibers and thephotonic integrated circuit to communicate light between the one or moreoptical fibers and the photonic integrated circuit. The fiber-opticconnector includes a polarization beam splitter and a patternedbirefringent plate. The polarization beam splitter is configured tosplit an incident light beam from a corresponding fiber core into afirst beam having a first polarization and a second beam having a secondpolarization different from the first polarization. The patternedbirefringent plate includes a first region and a second region, thefirst region has a first optical birefringence, the second region has asecond optical birefringence that is different from the first opticalbirefringence, the first region is produced by applying localizedheating to a portion of a birefringent plate to reduce the birefringenceat the first region, the second region is not subject to the localizedheating and retains its original birefringence. The polarization beamsplitter is configured to direct the first beam towards the first regionand direct the second beam towards the second region. The first regionis configured to rotate the polarization of the first beam by a firstamount, the second region is configured to rotate the polarization ofthe second beam by a second amount that is different from the firstamount, the first and second amounts are selected to cause the first andsecond beams to have substantially parallel polarization after passingthe patterned birefringent plate.

Implementations can include one or more of the following features. Thepatterned birefringent plate can be made from a single piece ofbirefringent material.

The first region can be an integral portion of the patternedbirefringent plate, and no glue or adhesive is used to bond the firstregion to other portions of the patterned birefringent plate.

The patterned birefringent plate has a top surface and a bottom surface,and the first region can extend from the top surface to the bottomsurface.

The patterned birefringent plate has a top surface and a bottom surface,and the first region can be positioned within the birefringent plate ata first distance from the top surface and a second distance from thebottom surface.

The patterned birefringent plate has a top surface and a bottom surface,and the first region can extend from the top surface to a locationwithin the birefringent plate at a distance from the bottom surface.

The polarization beam splitter can be configured to cause the secondpolarization of the second beam to be orthogonal to the firstpolarization of the first beam after the first and second beams exit thepolarization beam splitter. The first region can have substantially zerobirefringence, and the second region can be configured to rotate thepolarization of the second beam by about 90°+n×180°, 0≤n, n being aninteger.

The one or more optical fibers can include an array of at least 2 rowsand at least 8 columns of fiber cores. The patterned birefringent platecan include at least two first regions, each first region can have anelongated shape that extends along a direction parallel to the rowdirection. The second region can include the birefringent materialadjacent to the first regions. The polarization beam splitter can beconfigured to split 8 incident light beams from 8 corresponding fibercores of a row into 8 first beams having the first polarization and 8second beams having the second polarization, direct the 8 first beamstoward a first region, and direct the 8 second beams to the secondregion. Upon the 8 first beams passing through the first region and the8 second beams passing through the second region, the 8 first beams andthe 8 second beams can have substantially parallel polarization.

The one or more optical fibers can include an array of at least 2 rowsand at least 8 columns of fiber cores. The patterned birefringent platecan include an array of at least 2 rows and at least 8 columns of firstregions. The second region can include the birefringent materialadjacent to the first regions. The polarization beam splitter can beconfigured to split 8 incident light beams from 8 corresponding fibercores of a row into 8 first beams having the first polarization and 8second beams having the second polarization different from the firstpolarization, direct the 8 first beams toward 8 corresponding firstregions, and direct the 8 second beams towards the second region. Uponthe 8 first beams passing through the 8 first regions and the 8 secondbeams passing through the second region, the 8 first beams and the 8second beams can have substantially parallel polarization.

The fiber-optic connector can include a first connector part and asecond connector part, the first connector part can be removably coupledto the second connector part, the first connector part can be opticallycoupled to the plurality of fiber cores, the second connector part canbe optically coupled to the plurality of vertical-coupling elements, andboth the polarization beam splitter and the patterned birefringent platecan be included in the first connector part.

The fiber-optic connector can include a first connector part and asecond connector part, the first connector part can be removably coupledto the second connector part, the first connector part can be opticallycoupled to the plurality of fiber cores, the second connector part canbe optically coupled to the plurality of vertical-coupling elements, andboth the polarization beam splitter and the patterned birefringent platecan be included in the second connector part.

The fiber-optic connector can include a first connector part and asecond connector part, the first connector part can be removably coupledto the second connector part, the first connector part can be opticallycoupled to the plurality of fiber cores, the second connector part canbe optically coupled to the plurality of vertical-coupling elements, thepolarization beam splitter can be included in the first connector part,and the patterned birefringent plate can be included in the secondconnector part.

In another general aspect, an apparatus includes: a fiber-opticconnector configured to be connected between one or more optical fibershaving a plurality of fiber cores and a photonic integrated circuitincluding a plurality of vertical-coupling elements disposed along amain surface of the photonic integrated circuit. The fiber-opticconnector includes a polarization beam splitter and a patternedbirefringent plate. The polarization beam splitter is configured tosplit an incident light beam from a corresponding fiber core into afirst beam having a first polarization and a second beam having a secondpolarization different from the first polarization. The patternedbirefringent plate includes a first region and a second region, thefirst region has a first optical birefringence, the second region has asecond optical birefringence that is different from the first opticalbirefringence, the difference in the first and second opticalbirefringence is caused by performing at least one of (i) applyinglocalized heating to the first region without applying localized heatingto the second region to cause the first region to have a lowerbirefringence as compared to the second region, or (ii) applyingdifferent amounts of localized heating to the first and second regionsto cause the first region to have a first birefringence and the secondregion to have a second birefringence different from the firstbirefringence. The polarization beam splitter is configured to directthe first beam towards the first region and direct the second beamtowards the second region. The first region is configured to rotate thepolarization of the first beam by a first amount, the second region isconfigured to rotate the polarization of the second beam by a secondamount that is different from the first amount, the first and secondamounts are selected to cause the first and second beams to havesubstantially parallel polarization after passing the patternedbirefringent plate.

Implementations can include the following feature. The first region canbe an integral portion of the patterned birefringent plate, and no glueor adhesive is used to bond the first region to other portions of thepatterned birefringent plate.

In another general aspect, an apparatus includes: a first connector partthat is part of a fiber-optic connector configured to be connectedbetween one or more optical fibers having a plurality of fiber cores anda photonic integrated circuit including a plurality of vertical-couplingelements disposed along a main surface of the photonic integratedcircuit. The fiber-optic connector includes a polarization beamsplitter, and the first connector part includes a patterned birefringentplate. The polarization beam splitter is configured to split an incidentlight beam from a corresponding fiber core into a first beam having afirst polarization and a second beam having a second polarizationdifferent from the first polarization. The patterned birefringent plateincludes non-uniform birefringence produced by applying localizedheating to the birefringent plate to cause one or more regions of thebirefringent plate to have reduced birefringence as compared to one ormore other regions of the birefringent plate, resulting in at least onelower-birefringence region and at least one higher-birefringence regionin the patterned birefringent plate. The polarization beam splitter isconfigured to direct the first beam towards a lower-birefringence regionin the patterned birefringent plate and direct the second beam towards ahigher-birefringence region in the patterned birefringent plate. Thelower-birefringent region is configured to rotate the polarization ofthe first beam by a first amount, the higher-birefringent region isconfigured to rotate the polarization of the second beam by a secondamount that is different from the first amount, the first and secondamounts are selected to cause the first and second beams to havesubstantially parallel polarization after passing the patternedbirefringent plate.

Implementations can include one or more of the following features. Thelower-birefringence region can have substantially zero birefringence.

The first connector part can include the polarization beam splitter.

The lower-birefringence region can be an integral portion of thepatterned birefringent plate, and no glue or adhesive is used to bondthe lower-birefringence region to other portions of the patternedbirefringent plate.

In another general aspect, an apparatus includes: a patternedbirefringent plate that is part of a fiber-optic connector configured tobe connected between one or more optical fibers having a plurality offiber cores and a photonic integrated circuit including a plurality ofvertical-coupling elements disposed along a main surface of the photonicintegrated circuit. The patterned birefringent plate includesnon-uniform birefringence produced by applying localized heating to thebirefringent plate to cause one or more regions of the birefringentplate to have reduced birefringence as compared to one or more otherregions of the birefringent plate, resulting in at least onelower-birefringence region and at least one higher-birefringence regionin the patterned birefringent plate. The lower-birefringence region isconfigured to rotate the polarization of a first light beam by a firstamount, the higher-birefringence region is configured to rotate thepolarization of a second light beam by a second amount that is differentfrom the first amount, the first and second light beams are transmittedbetween one or more of the plurality of fiber cores and one or more ofthe vertical-coupling elements.

Implementations can include one or more of the following features. Thefiber-optic connector can include a first connector part removablycoupled to a second connector part, the first connector part can beoptically coupled to the plurality of fiber cores, the second connectorpart can be coupled to the vertical coupling elements, and the firstconnector part can include the polarization beam splitter.

The lower-birefringence region can have substantially zero birefringenceand can be configured to rotate the polarization of a first light beamby a substantially zero amount.

In another general aspect, an apparatus includes: a fiber-opticconnector configured to optically couple a plurality of optical fibersto a plurality of vertical coupling elements on a photonic integratedcircuit. The fiber-optic connector includes: a patterned birefringentplate including a plurality of first regions and a plurality of secondregions, the first regions including a material having birefringencethat is different from the birefringence of the material of the secondregions, the first and second regions forming an integrated piece ofoptical element. The fiber-optic connector is configured to enable lightbeams to be transmitted between the plurality of optical fibers and theplurality of vertical coupling elements, and the patterned birefringentplate is configured to modify an optical property of a selected portionof light that passes through the patterned birefringent plate.

Implementations can include the following feature. The patternedbirefringent plate can be configured to modify the polarization of afirst portion of the light that passes through the patternedbirefringent plate by a first amount, and modify the polarization of asecond portion of the light that passes through the patternedbirefringent plate by a second amount.

In another general aspect, an apparatus includes: a fiber-opticconnector configured to optically couple a plurality of optical fibersto a plurality of vertical coupling elements on a photonic integratedcircuit. The fiber-optic connector includes a patterned birefringentplate comprising non-uniform birefringence produced by chemical etchingone or more portions of a birefringent plate to cause the patternedbirefringent plate to have one or more first regions of birefringentmaterial having a first thickness and one or more second regions ofbirefringent material having a second thickness that is different fromthe first thickness. The fiber-optic connector is configured to enablelight beams to be transmitted between the plurality of optical fibersand the plurality of vertical coupling elements, and the patternedbirefringent plate is configured to modify an optical property of aselected portion of light that passes through the patterned birefringentplate.

Implementations can include one or more of the following features. Thefirst region can have a dimension in a range from 50 μm to 1000 μm, thedimension is measured along a plane parallel to a top surface of thepatterned birefringent plate.

The first region can have a dimension in a range from 100 μm to 600 μm,the dimension is measured along a plane parallel to a top surface of thepatterned birefringent plate.

The first region can have a dimension in a range from 200 μm to 400 μm,the dimension is measured along a plane parallel to a top surface of thepatterned birefringent plate.

The thickness of the birefringent material in the first region can besubstantially zero.

The patterned birefringent plate can be configured to modify apolarization state of a first set of light beams that pass through thefirst regions relative to a polarization state of a second set of lightbeams that pass through the second regions of the birefringent plate.

In another general aspect, a method includes: fabricating a fiber-opticconnector, including applying localized heating to a birefringent plateto produce a patterned birefringent plate. The localized heatingmodifies birefringence of a plurality of first regions in thebirefringent plate to cause the first regions to have birefringence thatis different from the birefringence of second regions that do notreceive the localized heating. The method includes aligning thepatterned birefringent plate to other optical components in thefiber-optic connector; and bonding the patterned birefringent plate tothe other optical components in the fiber-optic connector.

In another general aspect, a method of fabricating a fiber-opticconnector includes: applying localized heating to a birefringent plateto produce a patterned birefringent plate. The localized heatingmodifies birefringence of a plurality of first regions in thebirefringent plate to cause the first regions to have birefringence thatis different from the birefringence of second regions that do notreceive the localized heating. The method includes attaching thepatterned birefringent plate to a second component to form a fiber-opticconnector that is configured to be coupled to at least one of aplurality of optical fibers or a plurality of coupling elements on aphotonic integrated circuit.

Implementations can include one or more of the following features. Thelocalized heating can cause the first regions to have reducedbirefringence.

The localized heating can cause the first regions to have substantiallyzero birefringence.

Applying localized heating can include applying a laser beam to thefirst regions to locally heat the first regions.

The first regions can include elongated strips, the elongated strips canhave lengthwise directions that are parallel to one another, and thestrips can be spaced apart in a direction perpendicular to thelengthwise direction.

The patterned birefringent plate can include an array of at least 2 rowsand at least 8 columns of first regions.

Prior to applying the localized heating, the birefringent plate caninclude a crystalline quartz plate having predefined birefringence, andthe localized heating can produce amorphous fused silica havingmodified, lower, or substantially no birefringence in the first regions.

Applying localized heating can include sequentially applying localizedheating to the first regions one after another.

Applying localized heating can include applying localized heating tomultiple first regions in parallel.

The birefringent plate can be configured to modify a polarization stateof a first set of light beams that pass through the first regions of thebirefringent plate relative to a polarization state of a second set oflight beams that pass through the second regions of the birefringentplate.

Applying localized heating to the birefringent plate can includeapplying localized heating to the birefringent plate to modifybirefringence of a two-dimensional array of first regions in thebirefringent plate to cause the array of first regions to havebirefringence that is different from the birefringence of second regionsthat do not receive the localized heating, and the two-dimensional arraycan include at least 2 rows and at least 8 columns.

The spacing between two adjacent rows in the two-dimensional array canbe identical to the spacing between two adjacent columns in thetwo-dimensional array.

The fiber-optic connector can be configured to be optically coupled to atwo-dimensional array of optical fibers.

The fiber-optic connector can be configured to enable a first set oflight beams and a second set of light beams to be transmitted betweenthe two-dimensional array of optical fibers and a two-dimensional arrayof vertical coupling elements, and the birefringent plate can beconfigured to modify a polarization state of the first set of lightbeams that pass through the first regions of the birefringent platerelative to a polarization state of the second set of light beams thatpass through the second regions of the birefringent plate.

The fiber-optic connector can be configured to be optically coupled to atwo-dimensional array of vertical coupling elements on the photonicintegrated circuit.

The fiber-optic connector can be configured to enable a first set oflight beams and a second set of light beams to be transmitted between atwo-dimensional array of optical fibers and the two-dimensional array ofvertical coupling elements. The birefringent plate can be configured tomodify a polarization state of the first set of light beams that passthrough the first regions of the birefringent plate relative to apolarization state of the second set of light beams that pass throughthe second regions of the birefringent plate.

Each of at least some of the first regions can have a substantiallycircular, oval, triangular, square, or rectangular shape.

The two-dimensional array of first regions can include at least 2parallel strips, and applying localized heating to the birefringentplate can include applying localized heating to modify birefringence ofthe at least 2 parallel strips in the birefringent plate to cause the atleast 2 parallel strips to have birefringence that is different from thebirefringence of the second regions that do not receive the localizedheating.

Each strip can have a width in a range from 50 μm to 1000 μm.

Each strip can have a width in a range from 100 μm to 600 μm.

Each strip can have a width in a range from 200 μm to 400 μm.

The fiber-optic connector can be configured to be optically coupled to aplurality of vertical coupling elements on the photonic integratedcircuit, and the fiber-optic connector can be configured to enable thefirst set of light beams and the second set of light beams to betransmitted between the plurality of optical fibers and the plurality ofvertical coupling elements.

Applying the localized heating to the birefringent plate can includeapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions.

Applying the localized heating to the birefringent plate can includeapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions to substantially zero birefringence.

Applying the localized heating to the birefringent plate can includeapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions such that the second set of lightbeams that pass through the second regions have polarization that isrotated about 90°+n×180°, 0≤n, n being an integer, relative topolarization of the first set of light beams that pass through the firstregions.

The first optical connector part can include a walk-off elementconfigured to: receive a plurality of light beams from the plurality ofoptical fibers, split the light beams into first beam components andsecond beam components, the second beam components have polarizationthat is orthogonal to the polarization of the first beam components,direct the first beam components toward the first regions having lowerbirefringence, and direct the second beam components toward the secondregions having higher birefringence.

Applying the localized heating to the birefringent plate can includeapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions such that the second set of lightbeams that pass through the second regions have polarization that isrotated about 90°+n×180°, 0≤n, n being an integer, relative topolarization of the first set of light beams that pass through the firstregions. The walk-off element can be configured such that upon exitingthe walk-off element the first beam components have first polarization,and the second beam components have second polarization that issubstantially orthogonal to the first polarization. The first and secondregions of the birefringent plate can be configured such that afterpassing the first and second regions the first beam components havepolarization that is substantially parallel to the polarization of thesecond beam components.

The walk-off element can separate the first beam component and thesecond beam component along a walk-off direction, each of at least someof the first regions can have a dimension measured along a directionparallel to the walk-off direction in a range from 50 μm to 1000 μm.

Each of at least some of the first regions can have a dimension measuredalong a direction parallel to the walk-off direction in a range from 100μm to 600 μm.

Each of at least some of the first regions can have a dimension measuredalong a direction parallel to the walk-off direction in a range from 200μm to 400 μm.

Applying localized heating to the birefringent plate can includeapplying localized heating to the birefringent plate to modifybirefringence of the two-dimensional pattern of first regions in thebirefringent plate such that the birefringent plate is configured tomodify polarization of light passing the birefringent plate in a waythat is equivalent to modification of polarization of light passing ahalf-wave plate having openings at the two-dimensional pattern of firstregions.

The birefringent plate can include a first surface and a second surface.Applying localized heating to the birefringent plate can includeapplying localized heating to first regions that extend from the firstsurface to the second surface.

The birefringent plate can include a first surface and a second surface.Applying localized heating to the birefringent plate can includeapplying localized heating to first regions that are positioned withinthe birefringent plate and spaced at a first distance from the firstsurface and a second distance from the second surface.

The birefringent plate can include a first surface and a second surface,and the first surface can be closer to the plurality of optical fibersrelative to the second surface. Applying localized heating to thebirefringent plate can include applying localized heating to firstregions that extend from the first surface to a location inside thebirefringent plate, and the first regions can be spaced at a distancefrom the second surface.

The birefringent plate can include a first surface and a second surface,and the first surface can be closer to the plurality of couplingelements relative to the second surface. Applying localized heating tothe birefringent plate can include applying localized heating to firstregions that extend from the second surface to a location inside thebirefringent plate, and the first regions can be spaced at a distancefrom the first surface.

Applying localized heating can include using one or more laser beams toapply the localized heating.

In another general aspect, a method of fabricating a fiber-opticconnector includes: applying one or more particle beams to abirefringent plate to locally energize regions of the birefringent plateto produce a patterned birefringent plate. The localized energizingmodifies birefringence of a plurality of first regions in thebirefringent plate to cause the first regions to have birefringence thatis different from the birefringence of second regions that do notreceive the localized energizing. The method includes attaching thepatterned birefringent plate to a second component to form a fiber-opticconnector that is configured to be coupled to at least one of aplurality of optical fibers or a plurality of coupling elements on aphotonic integrated circuit.

In another general aspect, a method of fabricating a fiber-opticconnector includes: applying localized heating to a birefringent plateto modify birefringence of a two-dimensional array of first regions inthe birefringent plate to cause the array of first regions to havebirefringence that is different from the birefringence of second regionsthat do not receive the localized heating, the array including at least2 rows and at least 8 columns. The method includes coupling thebirefringent plate to a first connector part and a second connector partto form the fiber-optic connector. The first connector part isconfigured to be coupled to a plurality of optical fibers, and thesecond connector part is configured to be coupled to a photonicintegrated circuit. The first optical connector part includes a walk-offelement configured to: receive a plurality of light beams from theplurality of optical fibers, and split the light beams into first beamcomponents and second beam components, the second beam components havingpolarization that is orthogonal to the polarization of the first beamcomponents. The walk-off element is configured to direct the first beamcomponents toward the first regions having lower birefringence, anddirect the second beam components toward the second regions havinghigher birefringence.

Implementations can include one or more of the following features. Thebirefringent plate can be configured to modify a polarization state ofthe second beam components that pass through the second regions of thebirefringent plate relative to a polarization state of the first beamcomponents that pass through the first regions of the birefringentplate.

The second connector part can be configured to be optically coupled to atwo-dimensional array of vertical coupling elements on the photonicintegrated circuit, and the fiber-optic connector can be configured toenable light to be transmitted between the two-dimensional array ofoptical fibers and the two-dimensional array of vertical couplingelements.

Applying the localized heating to the birefringent plate can includeapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions.

Applying the localized heating to the birefringent plate can includeapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions to substantially zero birefringence.

Applying the localized heating to the birefringent plate can includeapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions such that the second beam componentsthat pass through the second regions have polarization that is rotatedabout 90°+n×180°, 0≤n, n being an integer, relative to polarization ofthe first beam components that pass through the first regions.

The walk-off element can be configured such that upon exiting thewalk-off element the first beam components have first polarization, andthe second beam components have second polarization that issubstantially orthogonal to the first polarization. The first and secondregions of the birefringent plate can be configured such that afterpassing the first and second regions the first beam components havepolarization that is parallel to the polarization of the second beamcomponents.

The walk-off element can separate the first beam component and thesecond beam component along a walk-off direction, and each of at leastsome of the first regions can have a dimension measured along adirection parallel to the walk-off direction in a range from 50 μm to1000 μm.

Each of at least some of the first regions can have a dimension measuredalong a direction parallel to the walk-off direction in a range from 100μm to 600 μm.

Each of at least some of the first regions can have a dimension measuredalong a direction parallel to the walk-off direction in a range from 200μm to 400 μm.

In another general aspect, a method of fabricating a fiber-opticconnector includes: applying localized heating or localized energizingto a birefringent plate to modify birefringence of a plurality of firstregions in the birefringent plate to cause each of at least some of theplurality of first regions to have a birefringence that is differentfrom the birefringence of second regions that do not receive thelocalized heating or localized energizing; and attaching thebirefringent plate to a first interface module and a second interfacemodule. The first interface module is configured to be coupled to aplurality of optical fibers, the second interface module is configuredto be coupled to a plurality of vertical coupling elements on a photonicintegrated circuit, the birefringent plate is positioned in opticalpaths between the first interface module and the second interfacemodule, and the birefringent plate is configured to modify an opticalproperty of light differently depending on whether the light passesthrough the first regions or the second regions.

Implementations can include one or more of the following features. Thefirst interface module can be configured to be coupled to atwo-dimensional array of optical fibers, the two-dimensional array caninclude at least 2 rows and at least 8 columns, the second interfacemodule can be configured to be coupled to a two-dimensional array ofvertical coupling elements, the birefringent plate can be configured tomodify a polarization state of a first set of light beams relative to asecond set of light beams that are transmitted between thetwo-dimensional array of optical fibers and the two-dimensional array ofvertical coupling elements.

After applying localized heating or localized energizing to thebirefringent plate, the birefringent plate can include a plurality offirst regions that have lower birefringence and a plurality of secondregions that have higher birefringence, the first regions alternatingwith the second regions. The first interface module can include awalk-off element configured to receive a plurality of light beams fromthe plurality of optical fibers, split each of at least some of thelight beams into a first beam component and a second beam component,direct the first beam component toward one of the first regions havingthe lower birefringence, and direct the second beam component toward oneof the second regions having the higher birefringence.

The walk-off element can be configured such that upon exiting thewalk-off element the first beam component has a first polarization, andthe second beam component has a second polarization that is orthogonalto the first polarization. The first and second regions of thebirefringent plate can be configured such that after passing the firstand second regions the first beam component has a polarization that isparallel to the polarization of the second beam component.

The walk-off element can separate the first beam component and thesecond beam component along a walk-off direction, each of at least someof the first regions can have a dimension measured along a directionparallel to the walk-off direction in a range from 50 μm to 1000 μm.

Each of at least some of the first regions can have a dimension measuredalong a direction parallel to the walk-off direction in a range from 100μm to 600 μm.

Each of at least some of the first regions can have a dimension measuredalong a direction parallel to the walk-off direction in a range from 200μm to 400 μm.

The walk-off element can be configured to direct a first beam componentof a light beam to a first region, direct a second beam component of thelight beam to a second region, and a center of the first region and acenter of the second region can be spaced apart at a distance in a rangefrom 50 μm to 1000 μm.

The center of the first region and the center of the second region canbe spaced apart at a distance in a range from 100 μm to 600 μm.

The center of the first region and the center of the second region canbe spaced apart at a distance in a range from 200 μm to 400 μm.

In another general aspect, a method includes: generating a birefringentplate by performing: attaching a birefringent element comprising anoptically birefringent material to a second optical element, andapplying a removal process to remove portions of the opticallybirefringent material at a plurality of first regions such that afterthe removal process the plurality of first regions have no opticallybirefringent material or have optically birefringent material withreduced thickness. The method includes attaching the birefringent plateto a first connector part and a second connector part to form thefiber-optic connector. The first connector part can be configured to becoupled to a plurality of optical fibers, the second connector part canbe configured to be coupled to a photonic integrated circuit, and thebirefringent plate can be positioned between the first connector partand the second connector part.

Implementations can include one or more of the following features. Thebirefringent plate can be configured to modify a polarization state of afirst set of light beams that pass through the first regions to apolarization state of a second set of light beams that pass throughsecond regions of the optically birefringent element that have opticallybirefringent material with an original thickness.

Applying the removal process can include etching the opticalbirefringent material at the plurality of first regions.

The method can include disposing an etch stop layer between theoptically birefringent element and the second optical element beforeetching the optical birefringent material. Etching the opticalbirefringent material at the plurality of first regions can includeetching the optical birefringent element at the plurality of firstregions until the etch stop layer is reached.

The etch stop layer can include an anti-reflective coating.

Removing portions of the optically birefringent element can includelaser ablation of the optical birefringent element at the plurality offirst regions.

Removing portions of the optically birefringent material can includemechanical removal of material from the optical birefringent element atthe plurality of first regions.

Removing portions of the optically birefringent material at theplurality of first regions can include removing portions of theoptically birefringent material at a two-dimensional array of firstregions, and the two-dimensional array includes at least 2 rows and atleast 8 columns.

The birefringent element can be attached to a first surface of thesecond optical element. Each of the first regions can have a shapesubstantially resembling a circle, an oval, a triangle, a square, arectangle, or a polygon having n sides, n being an integer greater than4, and the shape is measured along a plane parallel to the first surfaceof the second optical element.

Each first region can have a footprint that fits within a square havinga side in a range from 50 μm to 1000 μm.

Each first region can have a footprint that fits within a square havinga side in a range from 100 μm to 600 μm.

Each first region can have a footprint that fits within a square havinga side in a range from 200 μm to 400 μm.

The first optical connector part can include a walk-off elementconfigured to: receive a plurality of light beams from the plurality ofoptical fibers, split the light beams into first beam components andsecond beam components, direct the first beam components toward thefirst regions, and direct the second beam components toward secondregions that are not subject to the removal process.

Applying the removal process can include removing the birefringentmaterial or reducing the height of the birefringent material at thefirst regions such that the second set of light beams that pass throughthe second regions have polarization that is rotated about 90°+n×180°,0≤n, n being an integer, relative to polarization of the first set oflight beams that pass through the first regions.

The walk-off element can be configured such that upon exiting thewalk-off element the first beam components have first polarization, andthe second beam components have second polarization that issubstantially orthogonal to the first polarization. The first and secondregions of the birefringent plate can be configured such that afterpassing the first and second regions the first beam components havepolarization that is substantially parallel to the polarization of thesecond beam components.

The walk-off element can separate the first beam component and thesecond beam component along a walk-off direction, each of at least someof the first regions can have a dimension measured along a directionparallel to the walk-off direction in a range from 50 μm to 1000 μm.

Each of at least some of the first regions can have a dimension measuredalong a direction parallel to the walk-off direction in a range from 100μm to 600 μm.

Each of at least some of the first regions can have a dimension measuredalong a direction parallel to the walk-off direction in a range from 200μm to 400 μm.

Applying the removal process can include applying the removal process toremove portions of the optically birefringent material at the firstregions such that the birefringent plate is configured to modifypolarization of light passing through the birefringent plate in a waythat is equivalent to modification of polarization of light passingthrough a half-wave plate having openings at the first regions.

Generating the birefringent plate can include applying the removalprocess to generate strips of birefringent material each having anoriginal thickness, and each strip has a width in a range from 50 μm to1000 μm, and a length at least 2000 μm.

Each strip can have a width in a range from 100 μm to 600 μm, and alength at least 1200 μm.

Each strip can have a width in a range from 200 μm to 400 μm, and alength at least 800 μm.

In another general aspect, a method of fabricating a fiber-opticconnector includes: applying a particle beam to locally energizeportions of a birefringent plate to generate a patterned birefringentplate by modifying birefringence of a two-dimensional pattern of firstregions in the birefringent plate to cause the first regions to havebirefringence that is different from the birefringence of second regionsthat do not receive the localized energizing by the particle beam; andcoupling the patterned birefringent plate to a second component to formthe fiber-optic connector. The fiber-optic connector is configured to becoupled to at least one of a plurality of optical fibers or a pluralityof vertical coupling elements on a photonic integrated circuit, and thepatterned birefringent plate includes non-uniform birefringenceproperties with respect to light that passes through the patternedbirefringent plate.

In another general aspect, a method of fabricating fiber-opticconnectors includes: providing a first module including a plurality ofunsingulated lens arrays; and providing a second module including aplurality of unsingulated patterned birefringent plates. Each patternedbirefringent plate includes birefringent material, the patternedbirefringent plate includes a plurality of first regions having reducedor no birefringence as compared to a plurality of second regions. Themethod includes aligning the plurality of unsingulated lens arrays inthe first module to the plurality of unsingulated patterned birefringentplates in the second module; bonding the first module to the secondmodule to form a first assembly; and cutting the first assembly tosingulate the first and second modules to produce a plurality offiber-optic connector parts. Each fiber-optic connector part includes asingulated birefringent plate and a singulated lens array.

In another general aspect, a method of fabricating fiber-opticconnectors includes: providing a first module including a plurality ofunsingulated first connector units. Each first connector unit isconfigured to be coupled to a plurality of optical fibers. The methodincludes providing a second module including a plurality of unsingulatedpatterned birefringent plates. Each patterned birefringent plateincludes birefringent material, the patterned birefringent plateincludes a plurality of first regions having reduced or no birefringenceas compared to a plurality of second regions, and the second module hasa first side and a second side. The method includes aligning theplurality of unsingulated first connector units in the first module tothe plurality of unsingulated patterned birefringent plates in thesecond module; bonding the first module to the first side of the secondmodule; and providing a third module comprising a plurality ofunsingulated second connector units. Each second connector unit isconfigured to be coupled to a photonic integrated circuit. The methodincludes aligning the plurality of unsingulated second connector unitsin the third module to the plurality of unsingulated patternedbirefringent plates in the second module; bonding the third module tothe second side of the second module to form a first assembly; andcutting the first assembly to singulate the first, second, and thirdmodules to produce a plurality of fiber-optic connectors. Eachfiber-optic connector includes: a singulated birefringent plate, asingulated first connector unit, and a singulated second connector unit.

In another general aspect, an apparatus includes: a fiber-opticconnector configured to optically couple a plurality of optical fibersto a plurality of vertical coupling elements on a photonic integratedcircuit. The fiber-optic connector includes a patterned birefringentplate including an optically birefringent material, the birefringentplate having a plurality of first regions that have birefringence thatis different from the birefringence of second regions, the first regionsare formed by localized heating or localized energizing that modifiesthe birefringence of the first regions, and the second regions are notsubject to the localized heating or localized energizing. Thefiber-optic connector is configured to enable light beams to betransmitted between the plurality of optical fibers and the plurality ofvertical coupling elements, and the patterned birefringent plate isconfigured to modify an optical property of a first set of the lightbeams relative to the optical property of a second set of the lightbeams.

Implementations can include one or more of the following features. Thefirst regions can have reduced birefringence as compared to the secondregions.

The first regions can have substantially zero birefringence.

The patterned birefringent plate can be configured to modify apolarization state of a first set of light beams that pass through thefirst regions relative to a polarization state of a second set of lightbeams that pass through the second regions of the birefringent plate.

The patterned birefringent plate can include a plurality of strips ofbirefringent material that are spaced apart from one another, the firstset of light beams can pass through the plurality of strips ofbirefringent material, and the second set of light beams can passthrough spacing between the plurality of strips of birefringentmaterial.

The patterned birefringent element can be configured to rotate thepolarization of the first set of the light beams relative to thepolarization of the second set of the light beams by an amountsubstantially equal to 90°+n×180°, 0≤n, n being an integer.

The patterned birefringent element can be configured to modify two lightbeams that have polarizations orthogonal to each other prior to passingthrough the patterned birefringent element such that the two light beamshave polarizations parallel to each other after passing through thepatterned birefringent element.

The patterned birefringent element can be configured to modify two lightbeams that have polarizations parallel to each other prior to passingthrough the patterned birefringent element such that the two light beamshave polarizations orthogonal to each other after passing through thepatterned birefringent element.

The fiber-optic connector can include one or more walk-off elementsconfigured to receive one or more input optical beams from one or moreof the optical fibers, and separate each of at least some of the inputoptical beams into a first optical beam component having a firstpolarization and a second optical beam component having a secondpolarization. The patterned birefringent element can be configured tomodify the polarization of first optical beam component relative to thepolarization of second optical beam component such that the polarizationstate of the first optical beam component relative to the second opticalbeam component changes after the first and second optical beam componentpass through the patterned birefringent element.

In another general aspect, an apparatus includes: a fiber-opticconnector configured to optically couple a plurality of optical fibersto a plurality of vertical coupling elements on a photonic integratedcircuit. The fiber-optic connector includes a volume of birefringentmaterial, one or more portions of the volume of birefringent materialhas or have modified birefringence compared to other portions of thevolume of birefringent material, and light beams transmitted between theplurality of optical fibers and the plurality of vertical couplingelements pass through the volume of birefringent material. The volume ofbirefringent material is configured to modify a polarization state of afirst set of the light beams relative to a second set of the light beamssuch that the polarization state of the first set of the light beamsrelative to the second set of the light beams changes after the firstand second sets of light beams pass through the volume of birefringentmaterial.

Implementations can include one or more of the following features. Thevolume of birefringent material can include a plurality of strips ofbirefringent material that are spaced apart from one another, the firstset of light beams can pass through the plurality of strips ofbirefringent material, and the second set of light beams can passthrough spacing between the plurality of strips of birefringentmaterial.

The patterned birefringent element can be configured to rotate thepolarization of the first set of the light beams relative to thepolarization of the second set of the light beams by an amountsubstantially equal to 90°+n×180°, 0≤n, n being an integer.

The patterned birefringent element can be configured to modify two lightbeams that have polarizations orthogonal to each other prior to passingthrough the patterned birefringent element such that the two light beamshave polarizations parallel to each other after passing through thepatterned birefringent element.

The patterned birefringent element can be configured to modify two lightbeams that have polarizations parallel to each other prior to passingthrough the patterned birefringent element such that the two light beamshave polarizations orthogonal to each other after passing through thepatterned birefringent element.

The fiber-optic connector can include one or more walk-off elementsconfigured to receive one or more input optical beams from one or moreof the optical fibers, and separate each of at least some of the inputoptical beams into a first optical beam component having a firstpolarization and a second optical beam component having a secondpolarization. The patterned birefringent element can be configured tomodify the polarization of first optical beam component relative to thepolarization of second optical beam component such that the polarizationstate of the first optical beam component relative to the second opticalbeam component changes after the first and second optical beam componentpass through the patterned birefringent element.

The apparatus can include the photonic integrated circuit.

The vertical coupling elements can include vertical grating couplers.

The photonic integrated circuit can include optical waveguides that arecoupled to the vertical coupling elements.

In another general aspect, a data center including the apparatusdescribed above.

In another general aspect, a method of operating the apparatus describedabove.

In another general aspect, a method of operating the data centerdescribed above.

In another general aspect, a method of assembly the apparatus describedabove.

In another general aspect, a method of processing data using theapparatus described above.

In another general aspect, a method includes: transmitting light from aplurality of optical fiber cores to a polarization beam splitter; and atthe polarization beam splitter, splitting an incident light beam from acorresponding fiber core into a first beam having a first polarizationand a second beam having a second polarization different from the firstpolarization. The method includes directing the first and second beamstoward a patterned birefringent plate comprising a first region and asecond region. The first region has a first optical birefringence, thesecond region has a second optical birefringence that is different fromthe first optical birefringence, the first region is produced byapplying localized heating to a portion of a birefringent plate toreduce the birefringence at the first region, the second region is notsubject to the localized heating and retains its original birefringence,the first beam is directed towards the first region, the second beam isdirected towards the second region. The method includes at the first andsecond regions, rotating the polarization of the first beam by a firstamount and rotating the polarization of the second beam by a secondamount that is different from the first amount, the first and secondamounts are selected to cause the first and second beams to havesubstantially parallel polarization after passing the patternedbirefringent plate.

Implementations can include one or more of the following features. Theplurality of optical fiber cores can be arranged in a two-dimensionalarray.

The two-dimensional array can include at least 2 rows and at least 8columns.

The spacing between two adjacent rows in the two-dimensional array canbe identical to the spacing between two adjacent columns in thetwo-dimensional array.

This document discloses various embodiments of a connector assembly foroptically connecting one or more optical fibers and an array of verticalcoupling elements of a photonic integrated circuit (PIC). In a generalaspect, a method includes: providing a photonic integrated circuitincluding a plurality of vertical-coupling elements disposed along amain surface of the photonic integrated circuit; attaching an opticalsubassembly to the photonic integrated circuit; removably connecting afiber connector to a ferrule frame, wherein the fiber connector isattached to an array of optical fibers; aligning the ferrule frame tothe optical subassembly using an active alignment process; and securelyconnecting the ferrule frame to the optical subassembly after the activealignment process.

Implementations can include one or more of the following features. Theactive alignment process can include: transferring light between atleast one optical fiber in the array of optical fibers and the photonicintegrated circuit through the optical subassembly and at least one ofthe vertical-coupling elements, and adjusting a position of the ferruleframe relative to the optical subassembly based on at least onecharacteristic of the light transferred between the at least one opticalfiber and the photonic integrated circuit.

The method can include removing the fiber connector from the ferruleframe.

The ferrule frame can include an opening to allow light from the arrayof optical fibers to be transmitted to the optical subassembly.

The method can include passing a portion of the fiber connector throughthe opening of the ferrule frame and positioning an end of the fiberconnector in proximity to the optical subassembly.

Removably connecting the array of optical fibers to the ferrule framecan include at least one of (i) using one or more screws to secure thearray of optical fibers to the ferrule frame, (ii) using one or moreclamps to secure the array of optical fibers to the ferrule frame, (iii)using one or more magnets to connect the array of optical fibers to theferrule frame.

The array of optical fibers can include a two-dimensional array ofoptical fibers.

The two-dimensional array of optical fibers can include at least tworows of optical fibers.

The array of optical fibers can include at least 10 fiber cores.

The array of optical fibers can include at least 50 fiber cores.

The array of optical fibers can include at least 100 fiber cores.

The optical subassembly can include a first lens array, and the activealignment process can include projecting light from the array of opticalfibers through the first lens array, including passing light from atleast one of the optical fibers through a corresponding lens to acorresponding vertical-coupling element.

The optical subassembly can include a beam displacer, and the activealignment process can include projecting light from the array of opticalfibers through the first lens array and the beam displacer to the atleast one vertical-coupling element.

The optical subassembly can include a second lens array, and the activealignment process can include projecting light from the array of opticalfibers through the first lens array, the beam displacer, and the secondlens array to the at least one vertical-coupling element.

The optical subassembly can include a half wave plate, and the activealignment process can include projecting light from the array of opticalfibers through the first lens array, the beam displacer, the half waveplate, and the second lens array to the at least one vertical-couplingelement.

The fiber connector can include a first lens array, and the activealignment process can include projecting light from the array of opticalfibers through the first lens array, including passing light from atleast one of the optical fibers through a corresponding lens to acorresponding vertical-coupling element.

The optical subassembly can include a beam displacer, and the activealignment process can include projecting light from the array of opticalfibers through the first lens array and the beam displacer to the atleast one vertical-coupling element.

The optical subassembly can include a second lens array, and the activealignment process can include projecting light from the array of opticalfibers through the first lens array, the beam displacer, and the secondlens array to the at least one vertical-coupling element.

The optical subassembly can include a half wave plate, and the activealignment process can include projecting light from the array of opticalfibers through the first lens array, the beam displacer, the half waveplate, and the second lens array to the at least one vertical-couplingelement.

The active alignment process can include adjusting the position of theferrule frame relative to the optical subassembly to maximize an overallefficiency of light transfer between the array of optical fibers and thephotonic integrated circuit.

The ferrule frame can include at least one of glass, metal, or plastic.

The ferrule frame can include a material that is transparent orsemi-transparent to ultra-violet (UV) light, and securely connecting theferrule frame to the optical subassembly can include attaching theferrule frame to the optical subassembly using an UV-curing adhesive.

Adjusting the position of the ferrule frame relative to the opticalsubassembly can include adjusting the position of the ferrule framealong a plane substantially parallel to the main surface of the photonicintegrated circuit.

Adjusting the position of the ferrule frame along the planesubstantially parallel to the main surface of the photonic integratedcircuit can include at least one of (i) adjusting the position of theferrule frame along an x-axis relative to the main surface of thephotonic integrated circuit, (ii) adjusting the position of the ferruleframe along a y-axis relative to the main surface of the photonicintegrated circuit, or (iii) rotating the ferrule frame about a z-axisrelative to the main surface of the photonic integrated circuit. The x-and y-axes are substantially parallel to the main surface of thephotonic integrated circuit, and the z-axis is substantiallyperpendicular to the main surface of the photonic integrated circuit.

Adjusting the position of the ferrule frame relative to the opticalsubassembly can include adjusting a distance of an end of the fiberconnector relative to the optical subassembly.

Adjusting the position of the ferrule frame relative to the opticalsubassembly can include adjusting a tilt angle of an end surface of thefiber connector relative to the optical subassembly.

Aligning the ferrule frame to the optical subassembly can includealigning the ferrule frame to the optical subassembly with a precisionof at least 10 μm accuracy.

Aligning the ferrule frame to the optical subassembly can includealigning the ferrule frame to the optical subassembly with a precisionof at least 1 μm accuracy.

Aligning the ferrule frame to the optical subassembly can includealigning the ferrule frame to the optical subassembly with a precisionof at least 0.1 μm accuracy.

Each of the vertical-coupling elements can include at least one of asingle-polarization vertical grating coupler, a turning mirror, apolarization-diversity vertical grating coupler, a vertical cavitysurface emitting laser, a surface-normal modulator, or a photodiode.

The beam displacer can include a polarization-dependent optical element.

In another general aspect, an apparatus includes: a photonic integratedcircuit including a plurality of vertical-coupling elements disposedalong a main surface of the photonic integrated circuit; an opticalsubassembly attached to the photonic integrated circuit; and a ferruleframe that is configured to enable a fiber connector to be removablyconnected to the ferrule frame and aligned with the optical subassembly.The fiber connector is connected to an array of optical fibers, theoptical subassembly is configured to transfer light between the arrayoptical fibers and the vertical-coupling elements on the photonicintegrated circuit. The ferrule frame is aligned to the opticalsubassembly using an active alignment process in which light istransferred between at least one optical fiber in the array of opticalfibers and the photonic integrated circuit through the opticalsubassembly and at least one of the vertical-coupling elements, and aposition of the ferrule frame relative to the optical subassembly isadjusted based on at least one characteristic of the light transferredbetween the at least one optical fiber and the photonic integratedcircuit. The ferrule frame is securely connected to the opticalsubassembly after the active alignment process.

Implementations can include one or more of the following features. Theferrule frame can enable the array of optical fibers to be aligned withthe optical subassembly with a precision of at least 10 μm.

The ferrule frame can enable the array of optical fibers to be alignedwith the optical subassembly with a precision of at least 1 μm.

The ferrule frame can enable the array of optical fibers to be alignedwith the optical subassembly with a precision of at least 0.1 μm.

The optical subassembly can include a first lens array, and the ferrulemodule can be configured to align the array of optical fibers with thelens array.

The optical subassembly can include a beam displacer attached to thefirst lens array.

The optical subassembly can include a second lens array, the beamdisplacer can be positioned between the first lens array and the secondlens array, and the second lens array can be positioned between the beamdisplacer and the vertical-coupling elements.

The optical subassembly can include a half wave plate positioned betweenthe beam displacer and the second lens array.

The optical subassembly can include a birefringent plate having holes,and the birefringent plate can be positioned between the beam displacerand the second lens array.

The fiber connector can include a first lens array, and the ferrulemodule can be configured to align the first lens array with the opticalsubassembly.

The optical subassembly can include a beam displacer.

The optical subassembly can include a second lens array positionedbetween the beam displacer and the vertical-coupling elements.

The optical subassembly can include a half wave plate positioned betweenthe beam displacer and the second lens array.

The optical subassembly can include a birefringent plate having holes,and the birefringent plate can be positioned between the beam displacerand the second lens array.

Each optical fiber can include one or more fiber cores, the opticalsubassembly can include at least one lens configured to communicatelight with a single one of the fiber cores and a single one of thevertical-coupling elements.

Each optical fiber can include one or more fiber cores, the opticalsubassembly can include a plurality of optical waveguides, each opticalwaveguide optically connecting a respective one of the fiber cores and arespective one of the vertical-coupling elements.

At least some of the optical waveguides can be tapered.

The optical subassembly can include one or more polarization beamsplitters.

The optical subassembly can include one or more polarization-rotatingelements.

Each optical fiber can include one or more fiber cores, the opticalsubassembly can be configured to communicate light between a firstnumber of the fiber cores and a second number of the vertical-couplingelements, and the second number can be greater than the first number.

Each of the vertical-coupling elements can include at least one of asingle-polarization vertical grating coupler, a turning mirror, apolarization-diversity vertical grating coupler, a vertical cavitysurface emitting laser, a surface-normal modulator, or a photodiode.

The ferrule frame can include at least one of glass, metal, or plastic.

The ferrule frame can include a material that is transparent orsemi-transparent to ultra-violet (UV) light, and an UV-curing adhesivecan be used to securely attach the ferrule frame to the opticalsubassembly.

The beam displacer can include a polarization-dependent optical element.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, features, and benefits of various disclosed embodimentswill become more fully apparent, by way of example, from the followingdetailed description and the accompanying drawings, in which:

FIG. 1 shows a block diagram of an optical communication system in whichat least some embodiments can be practiced;

FIG. 2 shows a schematic side view of an integrated optical device thatcan be used in the optical communication system of FIG. 1 according toan embodiment;

FIGS. 3A-3G schematically show various examples of one or more fibersthat can be used in the optical communication system of FIG. 1 accordingto some embodiments;

FIG. 4 schematically shows an example array of fibers that can be usedin the optical communication system of FIG. 1 according to anembodiment;

FIG. 5 shows a schematic cross-sectional side view of a fiber-to-PICconnector arrangement that can be used in the integrated optical deviceof FIG. 2 according to an embodiment;

FIG. 6 shows a schematic cross-sectional side view of a fiber-to-PICconnector arrangement that can be used in the integrated optical deviceof FIG. 2 according to another embodiment;

FIG. 7 shows a schematic cross-sectional side view of a fiber-to-PICconnector arrangement that can be used in the integrated optical deviceof FIG. 2 according to yet another embodiment; and

FIGS. 8A and 8B show schematic cross-sectional side views of a part of afiber-to-PIC connector arrangement that can be used in the integratedoptical device of FIG. 7 according to some embodiments.

FIGS. 8C to 8E are diagrams of example operations of walk-off crystals.

FIG. 9 is a diagram of an example of a fiber-to-PIC connector.

FIG. 10A is a side view of an example of a polarization-diversityassembly.

FIG. 10B is a side view of an example of a fiber-to-PIC connector.

FIGS. 10C and 10D are top views of examples of thepolarization-diversity assembly.

FIG. 11A is a top view of an example of a fiber-to-PIC connector.

FIGS. 11B and 11C are diagrams showing examples of directions ofbeam-displacements by walk-off crystals.

FIG. 12 is a diagram of an example of a fiber-to-PIC connector.

FIG. 13A is a side view of an example of a polarization-diversityassembly.

FIG. 13B is a diagram of an optical fiber connector.

FIG. 13C is a top view of an example of a birefringent hole plate.

FIG. 13D is a top view of an example of an array of grating couplers.

FIGS. 14A to 18B show diagrams of examples of arrangements of gratingcouplers and corresponding birefringent hole plates.

FIGS. 19A to 20C show diagrams of examples of arrangements of fiberports, corresponding birefringent hole plates, and correspondingarrangements of grating couplers.

FIGS. 21A to 21D are diagrams of examples of birefringent hole plates.

FIG. 22 is a diagram of an array of grating couplers that enables activealignment during assembly.

FIG. 23 is a diagram of an example of a fiber-to-PIC connector.

FIGS. 24A and 24B are side view of examples of a fiber-to-PIC connector.

FIG. 24C is a diagram of an example of walk-off directions in thefiber-to-PIC connector.

FIG. 25 is a diagram of an example of an optical power supply thatprovides optical power through a single optical fiber.

FIGS. 26 and 27 are diagrams of examples of optical power supplies thatprovide optical power through multiple optical fibers.

FIG. 28 is a diagram of an example of a fiber-to-PIC connector.

FIGS. 29 and 30 are diagrams of wavelength division multiplexers.

FIGS. 31A to 32 are tables showing wavelength-division-multiplexed laneassignments.

FIG. 33A is a top view of an example of an optoelectronic device.

FIGS. 33B and 33C are side views of example configurations for theoptoelectronic device.

FIG. 34A is a side view of an example of a fiber-to-PIC connector.

FIG. 34B is a top view of an example of the fiber-to-PIC connector.

FIG. 35 is a diagram of an example of a fiber-to-PIC connector that canprocess wavelength division multiplexed optical signals.

FIG. 36 shows diagrams of examples of an arrangement of fiber ports, acorresponding birefringent hole plate, and a corresponding array ofgrating couplers.

FIG. 37 is a diagram showing an example of waveguide routing fromgrating couplers to on-PIC modulators.

FIG. 38 is a diagram of an example of a fiber-to-PIC connector that canprocess wavelength division multiplexed optical signals from multiplerows of optical fibers.

FIG. 39 is a diagram of an example of a fiber-to-PIC connector thatincludes a filter-based wavelength division demultiplexer andmultiplexer.

FIG. 40 is a diagram of an example of a fiber-to-PIC connector thatincludes an isolator.

FIG. 41 is a side view of an example of a fiber-to-PIC connector.

FIG. 42 is a top view and a side view of an example of a circularlyasymmetric (or rotationally asymmetric) optical lens.

FIG. 43 is a diagram showing a top view and a side view of an array ofcircularly asymmetric optical lenses

FIG. 44 is a diagram showing a top view and a side view of an array ofcircularly symmetric optical lenses

FIG. 45A is a diagram showing an example of a fiber-to-PIC connectorthat uses an array of circularly asymmetric optical lenses.

FIG. 45B is a diagram showing an example of a fiber-to-PIC connectorthat uses an array of circularly symmetric optical lenses

FIGS. 46A and 46B are diagrams showing examples of fiber-to-PICconnectors that each couples an array of grating couplers to a fiberarray with end facets polished at an angle.

FIG. 47 is a diagram of an example of a fiber-to-PIC connector thatincludes an array of circularly asymmetric lenses and an array ofcircularly symmetric lenses.

FIG. 48 is a diagram of an example of a fiber-to-PIC connector thatincludes an assembly of two different arrays of circularly asymmetriclenses.

FIG. 49 is a diagram of an example of a fiber-to-PIC connector thatincludes two arrays of circularly asymmetric lenses, a walk-off crystal,and a birefringent hole plate.

FIG. 50 shows a top view and a side view of an example of a patternedbirefringent plate.

FIG. 51 shows a top view and a side view of another example of apatterned birefringent plate.

FIG. 52A is a perspective view of an example of a patterned birefringentplate.

FIGS. 52B to 52D are side views of examples of patterned birefringentplates.

FIGS. 53A and 53B are diagrams showing examples of birefringent platesthat have patterns generated in the birefringent element.

FIG. 53C is a diagram showing incident light passing through a patternedbirefringent plate.

FIGS. 54 to 60 are diagrams of examples of optoelectronic dataprocessing systems that use circular polarization maintaining fibers.

FIGS. 61 to 64 are diagrams of examples of fiber-to-photonic integratedcircuit connectors.

FIG. 65 is a diagram of an example of a co-packaged optical module andan optical path for a light beam between a vertical-coupling element anda fiber core.

FIG. 66 shows a side view and a top view of an example of theco-packaged optical subassembly.

FIGS. 67A and 67B are diagrams showing that components in the opticalsubassembly can have several degrees of mechanical motion.

FIG. 68 is a diagram of an example of a process for assembling anoptical stack that includes the photonic integrated circuit, the opticalsubassembly, and a ferrule frame.

FIG. 69 is a top view of an example of the ferrule frame.

FIG. 70 is a diagram of an example fiber array ferrule adapter coupledbetween an MPO connector and an optical assembly.

DETAILED DESCRIPTION

To accommodate the growing need for chip-to-chip interconnectionbandwidths, the use of optical I/Os can be beneficial.

FIG. 1 shows a block diagram of a communication system 100 in which atleast some embodiments can be practiced. As shown, system 100 comprisesintegrated optical communication devices 101 ₁-101 ₆ suitablyinterconnected by optical fibers 102 ₁-102 ₁₁ establishing communicationpaths between the optical communication devices. Communication system100 can also comprise one or more external optical power supply modules103 producing continuous-wave (CW) light or producing one or more trainsof periodic or non-periodic optical pulses for use in one or more of theintegrated optical communication devices 101 ₁-101 ₆. Some end-to-endcommunication paths can pass through external optical power supplymodules 103 (e.g., see the shown communication path between devices 101₂ and 101 ₆). For example, the communication path between devices 101 ₂and 101 ₆ can be jointly established by optical fiber links 102 ₇ and102 ₈, whereby light from external optical power supply 103 ismultiplexed onto optical fiber links 102 ₇ and 102 ₈. Some end-to-endcommunication paths can pass through a multiplexing unit 104 (e.g., seethe shown communication path between devices 101 ₂ and 101 ₆). Forexample, the communication path between devices 101 ₂ and 101 ₆ can bejointly established by optical fiber links 102 ₁₀ and 102 ₁₁, wherebylight from external optical power supply 103 can be multiplexed withinmultiplexing unit 104 onto optical fiber links 102 ₁₀ and 102 ₁₁.

Various elements of communication system 100 can benefit from the use ofoptical interconnects, which can use photonic integrated circuitscomprising optoelectronic devices, co-packaged and/or co-integrated withelectronic chips comprising integrated circuits.

As used herein, the term “photonic integrated circuit” (or PIC) shouldbe construed to cover planar lightwave circuits (PLCs), integratedoptoelectronic devices, wafer-scale products on substrates, individualphotonic chips and dies, and hybrid devices. Example material systemsthat can be used for manufacturing various PICs can include but are notlimited to III-V semiconductor materials, silicon photonics,silica-on-silicon products, silica-glass-based PLCs, polymer integrationplatforms, Lithium Niobate and derivatives, nonlinear optical materials,etc. Both packaged devices (e.g., wired-up and/or encapsulated chips)and unpackaged devices (e.g., dies) can be referred to as PICs.

PICs are used for various applications in telecommunications,instrumentation, and signal-processing fields. A PIC typically usesoptical waveguides to implement and/or interconnect various circuitcomponents, such as optical switches, couplers, routers, splitters,multiplexers/demultiplexers, filters, modulators, phase shifters,lasers, amplifiers, wavelength converters, optical-to-electrical (O/E)and electrical-to-optical (E/O) signal converters, etc. A waveguide in aPIC is usually an on-chip solid light conductor that guides light due toan index-of-refraction contrast between the waveguide's core andcladding. A PIC typically comprises a planar substrate onto whichoptoelectronic devices are grown by an additive manufacturing processand/or into which optoelectronic devices are etched by a subtractivemanufacturing processes, e.g., using a multi-step sequence ofphotolithographic and chemical processing steps.

An “optoelectronic device” can operate on both light and electricalcurrents (voltages) and can include one or more of: (i) an electricallydriven light source, such as a laser diode; (ii) an optical amplifier;(iii) an optical-to-electrical converter, such as a photodiode; and (iv)an optoelectronic component that can control the propagation and/orcertain properties of light, such as an optical modulator or a switch.The corresponding optoelectronic circuit can additionally include one ormore optical elements and/or one or more electronic components thatenable the use of the circuit's optoelectronic devices in a mannerconsistent with the circuit's intended function. Some optoelectronicdevices can be implemented using one or more PICs.

As used herein, the term “integrated circuit” (IC) should be construedto encompass both a non-packaged die and a packaged die. In a typicalIC-fabrication process, dies (chips) are produced in relatively largebatches using wafers of silicon or other suitable material(s).Electrical and optical circuits can be gradually created on a waferusing a multi-step sequence of photolithographic and chemical processingsteps. Each wafer is then cut (“diced”) into many pieces (chips, dies),each containing a respective copy of the circuit that is beingfabricated. Each individual die can be appropriately packaged prior tobeing incorporated into a larger circuit or be left non-packaged.

The term “hybrid circuit” can refer to a multi-component circuitconstructed of multiple monolithic ICs and possibly some discretecircuit components, all attached to each other to be mountable on andelectrically connectable to a common base or carrier. A representativehybrid circuit can include (i) one or more packaged or non-packageddies, with some or all of the dies including optical, optoelectronic,and/or semiconductor devices, and (ii) one or more optional discretecomponents, such as connectors, resistors, capacitors, and inductors.Electrical connections between the ICs, dies, and discrete componentscan be formed, e.g., using patterned conducting (such as metal) layers,ball-grid arrays, solder bumps, wire bonds, etc. The individual ICs caninclude any combination of one or more respective substrates, one ormore redistribution layers (RDLs), one or more interposers, one or morelaminate plates, etc.

In some embodiments, individual chips can be stacked. As used herein,the term “stack” refers to an orderly arrangement of packaged ornon-packaged dies in which the main planes of the stacked dies aresubstantially parallel to each other. A stack can typically be mountedon a carrier in an orientation in which the main plains of the stackeddies are parallel to each other and/or to the main plane of the carrier.

A “main plane” of an object, such as a die, a PIC, a substrate, or anIC, is a plane parallel to a substantially planar surface thereof thathas the largest sizes, e.g., length and width, among all exteriorsurfaces of the object. This substantially planar surface can bereferred to as a main surface. The exterior surfaces of the object thathave one relatively large size, e.g., length, and one relatively smallsize, e.g., height, are typically referred to as the edges of theobject.

FIG. 2 shows a schematic cross-sectional side view of an exampleintegrated optical communication device 200 according to an embodiment.Device 200 can be used, e.g., to implement one or more of devices 101₁-101 ₆ of FIG. 1.

Device 200 comprises a PIC 210 that is based on any suitable PICtechnology/material platform, such as, without any implied limitation,Silicon Photonics, Indium Phosphide, or Lithium Niobate. PIC 210 hassupported on a substrate 201 thereof suitably connected passive opticalelements and/or arrays thereof, such as waveguides 220, couplers,splitters, filters, delay lines, etc., as well as optoelectronicelements and/or arrays thereof such as modulators, detectors, andtunable phase shifters. Some of these elements can be vertical-couplingelements 231, configured to couple light to/from the PIC. Herein, the“vertical” direction is a direction that is perpendicular to a mainsurface of the PIC. In the context of this disclosure, the term“vertical-coupling” denotes coupling at an angle that is substantiallyout-of-plane relative to a main surface of substrate 201, but notnecessarily perpendicular to said main surface. Vertical coupling istypically implemented at angles between 0 degrees (perpendicular) and 45degrees as measured from the surface-normal of the substrate's mainsurface. Vertical coupling can be performed from the top-side (e.g., thewaveguide-side) of the PIC (271 in FIG. 2) or form the bottom-side(e.g., the substrate-side) of the PIC (272 in FIG. 2).

In some embodiments, vertical-coupling elements 231 can be implemented,e.g., as turning mirrors, vertical grating couplers, elephant couplers,or as 3D vertical coupling structures that are 3D-printed onto the PIC,suitably connected to passive optical elements or to optoelectronicelements. In an example embodiment, vertical-coupling elements 231 canbe implemented, e.g., using any of the vertical-coupling elementsdisclosed in the following patent literature: US 2015/0037044, US2015/0125110, US 2015/0293305, U.S. Pat. No. 9,927,575, US 2018/0329159,US 2019/0258175, and U.S. Ser. No. 10/025,043. All of these U.S. Patentsand U.S. Patent Application Publications are incorporated herein byreference in their entirety.

In some embodiments, vertical-coupling elements 231 can besurface-normal optoelectronic elements such as surface-normalmodulators, surface-normal detectors, or surface-normal lasers, e.g.,vertical-cavity surface emitting lasers (VCSELs). In an exampleembodiment, vertical-coupling elements 231 can be implemented, e.g.,using any of the vertical-coupling elements disclosed in U.S. Patentsand U.S. Patent Application Publication(s) US 2019/0312642, U.S. Ser.No. 10/025,043, and U.S. Pat. No. 8,488,921, all of which areincorporated herein by reference in their entirety.

Vertical-coupling elements 231 can be geometrically variously arrangedin arrays 230 of such vertical-coupling elements.

In some embodiments, some optical or optoelectronic elements can bespatially co-located or interspersed with some vertical-couplingelements 231 of array 230.

In some embodiments, some optical or optoelectronic elements can belocated in areas of the PIC disjoint from vertical-coupling arrays 230.

Optical and optoelectronic elements of the PIC are suitably connected toelectronic integrated circuits 260, such as driver amplifiers,transimpedance amplifiers, electronic control circuits, digital logic,microcontrollers, microprocessors, and/or electronic switches. Someelectronic circuits can be spatially co-located or interspersed withsome vertical-coupling elements of arrays 230, and some electroniccircuits can be located in areas that are spatially disjoint from arrays230. Some electronic circuits can be monolithically integrated withoptical or optoelectronic elements of the PIC. Some electronic circuitscan be on a separate chip from the PIC and can be electrically connectedto the PIC using suitable electrical interconnect technologies, such asbond wires, balls, bumps, micro-bumps, pillars, and membranes, e.g., inthe form of a stack.

Of particular interest in the context of this disclosure are connectorstructures 271 and 272 that enable (possibly pluggable and/or removable)connection(s) between M spatial paths of one or more optical fibers 202as part of optical fiber links 102, and N vertical-coupling elements ofan array 230 of a PIC. In some embodiments, the numbers N and M aredifferent integers greater than one. In some other embodiments, N=M.

In the context of this disclosure, the term “spatial path” refers to anoptical path through a core of a single-mode or multi-mode opticalfiber, a core of a multi-core fiber, or one or more spatially coupledcores of a few-mode optical fiber configured to carry different signalsin its different spatial modes. A spatial path can carry signals in oneor more polarizations and/or on one or more wavelengths. In someembodiments, a spatial path can be polarization-maintaining. The one ormore optical fibers 202 can comprise single-mode, multi-mode, few-mode,multi-core, and/or polarization-maintaining fibers. The one or moreoptical fibers 202 can comprise dispersion-shifted,dispersion-compensating, non-zero-dispersion-shifted,standard-single-mode-dispersion, and/or high-dispersion fiber. The oneor more fibers 202 can be fixedly attached (e.g., glued) to connectorelements 250, e.g., by positioning individual fibers in individual holesprovided within connector elements 250, or by positioning individualfibers in a linear array of V-grooves and stacking multiple such lineararrays to form a 2D array. The M spatial paths of one or more fibers 202can, as a result, form an array with a certain geometrical layout andwith a certain separation of spatial paths in fiber end face planes 243.Fiber end face planes 243 can be parallel to a main surface of the PIC(e.g., as indicated in the shown details of structure 271, FIG. 2) orcan be at a non-zero angle relative to a main surface of the PIC (e.g.,as indicated in the shown details of structure 272, FIG. 2). In variousembodiments, said angle relative to the main surface of the PIC can beappropriately chosen between 0 degrees (in which case the correspondingfiber end face plane is parallel to the main surface of the PIC) and 90degrees (in which case the corresponding fiber end face plane isperpendicular to the main surface of the PIC).

Connector elements 240 can be fixedly attached (e.g., glued) to PIC 210,e.g., by aligning and subsequently affixing the connector elements toPIC 210 during assembly. Connector elements 240 can be attached toeither of the two main surfaces of PIC 210. Connector elements 240 canbe fixedly or movably attached to connector elements 250 in connectormating planes 241. Connector mating planes 241 can be parallel to a mainsurface of the PIC (e.g., as in structure 271 of FIG. 2) or can be at anangle relative to a main surface of the PIC (e.g., as in structure 272of FIG. 2). Said angle relative to the main surface of the PIC can bechosen between 0 degrees (in which case the corresponding connectormating plane is parallel to the main surface of the PIC) and 90 degrees(in which case the corresponding connector mating plane is perpendicularto the main surface of the PIC). In some embodiments, connector elements240 and 250 can comprise mechanical structures that enable elements 240and 250 to self-align. For example, such mechanical structures can beimplemented using cylindrical or conical post-and-hole arrangements,rod-and-groove arrangements, or ball-and-hole arrangements. Connectorelements 240 and 250 can further comprise mechanical structures capableof holding elements 240 and 250 in place after mating, e.g., a suitablesnap-on mechanism.

Either of connector elements 240 and 250 can contain one or more of: (i)reflective optical elements, such as dielectric or metallic interfaces;(ii) refractive optical elements, such as lenses or prisms; (iii)diffractive optical elements, such as gratings; (iv) birefringentoptical elements, such as calcite crystals, polarization gratings, orwaveplates; (v) 3D-waveguides or nanostructures written into a suitablehost material, such as glass; and/or (vi) 3D-printed optical waveguides,microstructures, or nanostructures. The combination of connectorelements 240 and 250 is typically designed to suitably map M spatialpaths of one or more optical fibers 202 in fiber end face planes 243 toN vertical-coupling elements of array 230 in coupling plane 242.Together, the corresponding set of fibers 202, connector elements 240and 250, and vertical coupling array 230 form a connector assembly 271or 272. Some embodiments disclosed herein are specifically directed atproviding optimized designs of connector assemblies 271 and 272, e.g.,with respect to tolerances in manufacturing, assemblage, and operation.Some of such embodiments can be scalable to a relatively large number ofspatial paths, e.g., M>100.

FIGS. 3A-3G illustrate configurations of one or more optical fibers 202according to some embodiments. More specifically, FIGS. 3A-3Gschematically show example cross-sectional views of one or more fibers202 in fiber coupling planes 243 according to various embodiments.

FIG. 3A illustrates a one-dimensional (1D) array of single-core,single-mode optical fibers supporting M=6 spatial paths. Each of theshown six fibers comprises a respective cladding 301 and a respectivecore 302, typically made from glasses of different refractive indicessuch that the refractive index of the cladding is lower than therefractive index of the core to establish a dielectric opticalwaveguide. More complex refractive index profiles, such as indextrenches, multi-index profiles, or gradually changing refractive indexprofiles can also be used in some embodiments. More complex geometricstructures such as non-circular cores or claddings, photonic crystalstructures, photonic bandgap structures, or nested antiresonant nodelesshollow core structures can also be used in some embodiments. For any ofthese structures, geometrical, structural, and material properties canbe appropriately chosen to allow for the propagation of a single guided(e.g., transverse) mode within the operating wavelength range of system100. In the context of this disclosure, three feature sizes are ofparticular interest: (i) an effective core diameter D_(core), typicallydefined as the diameter at which the optical intensity of the modepropagating within the fiber has dropped to 1/e² of its value at thecore center (sometimes also referred to as the mode field diameter);(ii) a minimum core-to-core spacing S_(min) within the array; and (iii)a maximum core-to-core spacing S_(max) within the array. The featuresizes D_(core), S_(min), and S_(max) corresponding to this particularembodiment are indicated in FIG. 3A.

FIG. 3B illustrates a two-dimensional (2D) array of single-core,single-mode optical fibers supporting M=12 spatial paths. The featuresizes S_(min) and S_(max) corresponding to this particular embodimentare indicated in FIG. 3B.

FIG. 3C illustrates a two-dimensional (2D) array of single-core,single-mode optical fibers supporting M=17 spatial paths. The featuresizes S_(min) and S_(max) corresponding to this particular embodimentare indicated in FIG. 3C.

Although only three example geometrical array layouts and spacings areshown in FIGS. 3A-3C, other geometrical array layouts can also be usedin various alternative embodiments. Based on the provided description, aperson of ordinary skill in the art will be able to make and use suchother geometrical array layouts without any undue experimentation. Someembodiments can also be constructed using one or more arrays of fiberswith dissimilar properties, such as a mixture of fibers with differentindex profiles, different effective core diameters, etc.

FIG. 3D illustrates a multi-core, single-mode optical fiber supportingM=7 spatial paths. The multi-core fiber comprises a cladding 301 andseven cores 302, typically made from glasses of different refractiveindices such that the refractive index of the cladding is lower than therefractive index of the core. More complex refractive index profiles,such as index trenches, multi-index profiles, or gradually changingrefractive index profiles, can also be used in some embodiments. Morecomplex geometric structures, such as non-circular cores, non-circularcladdings, photonic crystal structures, photonic bandgap structures, ornested antiresonant nodeless hollow core structures, can also be used.For any of these structures, geometrical, structural, and materialproperties can be chosen to allow for the propagation of a single guided(e.g., transverse) mode per core within the operating wavelength rangeof system 100. Regardless of their complexity, an effective corediameter D_(core) can be defined for each core. Different cores within afiber can have nominally identical or substantially different (e.g., bymore than 10%) effective core diameters. The feature sizes D_(core),S_(min), and S_(max) corresponding to this particular embodiment areindicated in FIG. 3D.

FIG. 3E illustrates a multi-core, single-mode optical fiber supportingM=4 spatial paths. The feature sizes S_(min) and S_(max) correspondingto this particular embodiment are indicated in FIG. 3E.

FIG. 3F illustrates a multi-core, single-mode optical fiber supportingM=8 spatial paths. The feature sizes S_(min) and S_(max) correspondingto this particular embodiment are indicated in FIG. 3F.

FIG. 3G illustrates a multi-core, single-mode optical fiber supportingM=4 spatial paths. The feature sizes S_(min) and S_(max) correspondingto this particular embodiment are indicated in FIG. 3G.

Although only four example geometrical core layouts and spacings areshown in FIG. 3D-3G, other geometrical core layouts can also be used invarious alternative embodiments. Based on the provided description, aperson of ordinary skill in the art will be able to make and use suchother geometrical core layouts without any undue experimentation.

FIG. 4 illustrates a configuration of one or more optical fibers 202according to some embodiments. More specifically, FIG. 4 schematicallyshows an example cross-sectional view of one or more fibers 202 in fibercoupling planes 243 according to various embodiments. FIG. 4 illustratesan example two-dimensional (2D) array of multi-core, single-mode opticalfibers supporting M=90 spatial paths. In some embodiments, differentfibers within the array can have different respective core counts,different respective effective core diameters, and/or differentrespective rotational orientations. The feature sizes S_(min) andS_(max) corresponding to this particular embodiment are indicated inFIG. 4.

In some embodiments, some cores of some multi-core fibers shown in FIGS.3D-3H and FIG. 4 can be designed to be substantially un-coupled, e.g.,exhibit a core-to-core crosstalk lower than 20 dB over 1 km ofpropagation distance, or can be designed to be relatively stronglycoupled. Some cores of single-core and/or multi-core fibers shown inFIGS. 3 and 4 can be designed to be few-moded or multi-moded, i.e. canbe designed to propagate a relatively small number (e.g., <10) or arelatively large number (e.g., ≥10) of transverse modes.

An important additional aspect of coupling a large number of spatialpaths from fibers 202 to a PIC 210 can include the consideration ofrelative sizes of practically usable fibers and optical, optoelectronic,and electronic elements, and their placement within the correspondinglarge arrays. For example, relatively close needed spacing(s) in someareas of the PIC may indicate that forming larger arrays may bedifficult, which poses a difficult scalability problem. In addition, insome cases, the relative alignment of a typical fiber core and a typicalvertical grating coupler may require a placement accuracy on the orderof 1 micron or better to achieve low coupling losses. However, suchrequirements may not be compatible with the typical accuracies achievedusing conventional passive alignment processes, which maydisadvantageously necessitate the use of slower and/or more expensiveactive alignment processes.

Having studied some of the shortcomings of existing fiber-to-PICcoupling structures, I have identified and examined, through analyses,modeling, and simulations, various designs of optical couplingstructures for removable fiber-to-PIC connections suitable forhigh-volume manufacturing of arrays supporting a large number of spatialpaths. In particular, the contemplated solutions can allow for efficientcoupling between M spatial paths of one or more optical fibers 202 andan array 230 of N vertical-coupling elements by implementing some or allof the following features: (i) magnifying or de-magnifying by a firstfactor (denoted as A) the minimum core-to-core spacing of optical fibersin fiber end face plane 243 to match the minimum spacing betweenvertical-coupling elements in coupling plane 242; (ii) magnifying orde-magnifying by a second factor (denoted as B) the maximum core-to-corespacing of optical fibers in fiber end face plane 243 to match themaximum spacing between vertical-coupling elements in coupling plane242; (iii) magnifying or de-magnifying by a third factor (denoted as C₁)the effective core diameter of optical fibers in fiber end face plane243 to match the effective vertical grating coupler sizes in couplingplane 242; (iv) magnifying or de-magnifying by a fourth factor (denotedas C₂) the effective core diameter of optical fibers in fiber end faceplane 243 to achieve a substantially different (e.g., larger) effectivebeam diameter in connector mating plane 241 than in fiber end face plane243; and/or (v) changing the effective cross-sectional geometricallayout of the plurality of spatial paths in at least some regionsbetween fiber end face plane 243, connector mating plane 241, andcoupling plane 242. In an example embodiment, at least some or all ofthe factors A, B, C₁, and C₂ can be different.

For an example of possible benefits that can be obtained, one mayconsider an example embodiment in which A=B=2 and C₁=1.5. In thisparticular embodiment, the scaling by C₁ allows for relaxed alignmenttolerances of the connector component 240 to be attached to a PIC 210.The scaling by A and B allows for even more relaxed optical waveguidespacings within the PIC 210, thereby potentially lowering thewaveguide-to-waveguide crosstalk and/or enabling the use of relativelylarge arrays.

FIG. 5 shows a fiber-to-PIC connector arrangement 500 that can be usedin device 200 (FIG. 2) according to an embodiment. As shown, connectorarrangement 500 comprises an array 501 of multi-core fibers (MCFs) 202connected to connector element 250. The end faces of the MCFs 202 arearranged to be substantially in the same plane, i.e., fiber end faceplane 243 (also see FIG. 2). Connector element 250 is further connectedto connector element 240, and the interface between the two connectorelements includes connector mating plane 241 (also see FIG. 2).

Connector element 250 includes one collimating lens 551 per MCF 202. Inan example embodiment, collimating lenses 551 can be arranged to provideenlarged light-beam-spot sizes in connector mating plane 241. Forexample, an effective core diameter of 10 micron together with the focallength f₁ of collimating lens 551 being f=500 micron can result in aneffective beam diameter of approximately 100 micron in connector matingplane 241.

Connector element 240 includes one focusing lens 541 per MCF 202. Thelongitudinal sizes of connector elements 240 and 250 can be selectedsuch as to have the connector mating plane 241 at any convenientposition between collimating lenses 551 and focusing lenses 541. Forexample, such sizes can be selected such as to achieve an expansion ofthe beam diameter in connector mating plane 241 by a factor of C₂≈10.Such expansion can be beneficial in that it can significantly simplifythe connector alignment. In alternative embodiments, other longitudinalsizes can similarly be selected to realize other values of the factor ofC₂.

In the example embodiment shown in FIG. 5, each focusing lens 541 has afocal length f₂=2f₁. This ratio of focal lengths results in amagnification of each MCF's entire core pattern by a factor of A=2 incoupling plane 242. For example, the minimum core-to-core spacingS_(min) (e.g., see FIG. 3D) is magnified in coupling plane 242 by afactor of two as well. This magnification applies both to the spacing(s)of the MCF cores and to the characteristic mode size(s) corresponding toeach individual core.

In order to independently choose the effective magnification applied toan individual spatial path, between fiber end face plane 243 andcoupling plane 242, each spatial path is directed through a respectiveindividual lens 542. For example, in the embodiment of FIG. 5, eachindividual lens 542 has a focal length f₃=70 micron and hence relativelyde-magnifies by 75%. As a result the overall characteristic-mode-sizemagnification C₁=2×0.75=1.5 is achieved. The larger effective mode sizein coupling pane 242 compared to fiber end face plane 243 canadvantageously help to relax the positioning tolerances of connectorelement 240 relative to the array of vertical coupling elements 230 incoupling plane 242.

In some embodiments, some or all lenses 542 can be laterally offset fromthe centers of the corresponding impinging light beams. Such lateraloffsets cause the light beams 543 that are directed toward thevertical-coupling elements 231 of array 230 to impinge at said couplingelements at a desired coupling angle, e.g., not necessarily along thenormal with respect to the corresponding PIC's main surface. Note thatthe maximum core-to-core spacing is left substantially unchanged in thisexample, as the applied magnification occurs on a per-MCF basis, therebyimplementing the B value of B≈1.

In the above-described example, the geometry-scaling parameter set {A,B, C₁, C₂} is approximately {2, 1, 1.5, 10}. However, other numericalcombinations for the geometry-scaling parameter set {A, B, C₁, C₂} arealso achievable, e.g., through proper selection of relevant sizes,positions, and focal lengths. From the above description, a person ofordinary skill in the art will be able to achieve such other numericalcombinations, as needed, without any undue experimentation.

Furthermore, the lens system illustrated by FIG. 5 represents only oneof many possible ways to perform independent array pattern scaling andmode size scaling using refractive optical elements. For example, agiven array pattern scaling can take place over any distinct subset ofspatial paths corresponding to fiber end face plane 243. Differentsubsets can have identical or different respective magnificationfactors. When individual subsets are differently scaled, the overallarray pattern geometry of fiber end face plane 243 can be transformed toyield a geometrically dissimilar array pattern in coupling plane 242.

In some embodiments, pattern scaling can also take place over the entireset of spatial paths corresponding to fiber end face plane 243, e.g., byusing a single lens element 551 that laterally spans the entire array501, thereby yielding in coupling plane 242 a geometrically similar,scaled image of array 501, as the latter is presented to the lens systemin fiber end face plane 243. An example embodiment using this design canachieve a parameter set {A, B, C₁, C₂} of {2, 2, 1.5, 10}.

In some embodiments, mode field diameter scaling can take place over anysubset of spatial paths corresponding to fiber end face plane 243 andcan use identical or different respective scaling (e.g., magnification)factors for different spatial paths.

In some embodiments, aspheric lenses and arrays thereof can be used.Such lenses can be manufacturable, e.g., using wafer-scale processingtechnologies.

In some embodiments, the functionalities of lenses 541 and 542 can becombined into a single aspheric refractive element, which can be 3Dprinted using technologies, such as those offered for sale by Nanoscribeof Eggenstein-Leopoldshafen, Germany.

As will be understood by people of ordinary skill in the art, settingthe angle of the fibers 202 relative to the PIC's main plane as well aschoosing the incidence angles of the individual light beams 543 ontovertical coupler array 230 are also possible, e.g., by mounting fibers202 in a slanted or bent fashion within connector element 250, slantingthe connector mating plane 241 at an angle relative to the PIC's mainplain, and/or introducing at suitable locations within assembly 500metallic or dielectric reflective interfaces, refractive elements, suchas prisms, and/or diffractive elements such as gratings.

FIG. 6 shows a fiber-to-PIC connector arrangement 600 that can be usedin device 200 (FIG. 2) according to another embodiment. As shown,connector arrangement 600 comprises an array 501 of MCFs 202 connectedto connector element 250. The end faces of the MCFs 202 are arranged tobe substantially in the same plane, i.e., fiber end face plane 243 (alsosee FIG. 2). Connector element 250 is further connected to connectorelement 240, and the interface between the two connector elementsincludes connector mating plane 241 (also see FIG. 2).

Connector element 250 includes an array of 3D waveguides 652, formed in(e.g., optically written in) a suitable host material such as glassusing a suitable technology, such as some of the products offered forsale by Optoscribe of Livingston, United Kingdom.

In some embodiments, 3D waveguides 652 written into connector element250 can expand or suitably geometrically re-arrange the array geometryof spatial paths provided by fibers 202 at fiber end face plane 243. Inthe embodiment shown in FIG. 6, 3D waveguides expand the mode fielddiameter by a factor of C₂=2 between fiber end face plane 243 andconnector mating plane 241.

In some embodiments, 3D waveguides 652 of connector element 250 canindependently expand the mode field diameter of individual waveguides toenable an expanded-beam connection at connector mating plane 241. Thiscan be accomplished by using taper or inverse-taper structures within 3Dwaveguide arrangement 652 and/or by changing one or more 3D waveguidewriting parameters, such as scan speed or repetition rate of thefemtosecond laser pulses used to write 3D waveguides 652, resulting inlarger 3D waveguide mode field diameters.

In some embodiments, 3D waveguides 652 in connector element 250 can alsointroduce bend angles, e.g., to accommodate different angles ofincidence of light from fibers 202, e.g., from a fiber end face planethat is not parallel to the PIC's main surface. In some embodiments,3D-waveguide bends can be combined with reflective or refractive anglechanges due to suitably placed dielectric or metallic interfaces (notexplicitly shown in FIG. 6), or diffractive angle changes from suitablyplaced gratings (not explicitly shown in FIG. 6).

Connector element 240 can use 3D waveguides 644 some of whose mode fielddiameters relative to a typical fiber mode field diameter within fiberend face plane 243 are expanded at connector mating pane 241 toessentially match the mode field diameter of the correspondingwaveguides of connector element 250 at connector mating plane 241.

In some embodiments, 3D waveguides 644 of connector element 240 cansuitably change array size, array geometry, mode size, and incidenceangles to match the respective geometric parameters at coupling plane242.

In the example embodiment shown in FIG. 6, each waveguide mode fielddiameter is reduced from a magnification of C₂=2 at connector matingplane 241 to 75% thereof, thereby yielding an overall mode fielddiameter magnification from fibers 202 in fiber end face plane 243 tovertical coupler array 230 in coupling plane 242 of C₁=2×0.75=1.5. Thelarger effective mode size in coupling plane 242 compared to fiber endface plane 243 can advantageously help to relax the positioningtolerances of connector element 240 relative to the array 230 ofvertical-coupling elements 231 in coupling plane 242.

In some embodiments, some or all waveguide bends 645 can establish adesired coupling angle to vertical-coupling elements 231 of array 230.

The 3D waveguide system described above should only be viewed as one ofmany possible embodiments that can be used to perform independent arraypattern scaling, array pattern geometry transformation, spot sizescaling, and angle-of-incidence adaptation. Hybrid assemblies are alsopossible in some embodiments and can be considered as functionalequivalents of the above-described embodiments. Some embodiments can useany suitable combination of diffractive, reflective, or refractivesurfaces, 3D waveguides, and 3D-printed structures within either or bothof connector elements 240 and 250.

Some embodiments can be constructed to use polarization diversity opticswithin connector assemblies 271 and 272. For example, some cores of theone or more fibers 202 can carry signals of random polarization or cancarry polarization-multiplexed signals. In addition, some verticalgrating couplers can be polarization sensitive. Properly couplingdual-polarization light from one or more fibers 202 to a PIC 210 canthus benefit from polarization-diversity vertical-coupling elements,such as two-dimensional polarization-diversity vertical gratingcouplers. Some polarization-diversity vertical-coupling elements canhave an inherently higher insertion loss compared to that ofsingle-polarization vertical-coupling elements. Hence, replacing onepolarization-diversity vertical-coupling element by a pair ofsingle-polarization vertical-coupling elements and performingpolarization-diversity outside the PIC, e.g., within connector assembly271 and 272, can be beneficial.

Some embodiments can benefit from the use of polarization diversityoptics disclosed, e.g., in U.S. Patent U.S. Pat. No. 9,927,575, which isincorporated herein by reference in its entirety.

FIG. 7 shows a fiber-to-PIC connector arrangement 700 that can be usedin device 200 (FIG. 2) according to yet another embodiment. As shown,connector arrangement 700 comprises an array 501 of MCFs 202 connectedto connector element 250. The end faces of the MCFs 202 are arranged tobe substantially in the same plane, i.e., fiber end face plane 243 (alsosee FIG. 2). Connector element 250 is further connected to connectorelement 240, and the interface between the two connector elementsincludes connector mating plane 241 (also see FIG. 2).

The embodiment shown in FIG. 7 is constructed to couple M=8 spatialpaths of fibers 202 in fiber end face plane 243 to N=16>Mvertical-coupling elements 231 of array 230.

Connector element 250 includes one collimating lens 551 per MCF 202. Inan example embodiment, collimating lenses 551 can be arranged to provideenlarged light-beam-spot sizes in connector mating plane 241. Connectorelement 250 further includes a polarization-diversity assembly 757.

FIG. 8A shows the schematic side-view 810 of a sub-element ofpolarization-diversity assembly 757 according to an embodiment. Asshown, assembly 757 comprises a birefringent beam displacement element753 (also referred to as a “walk-off element.” In some embodiments,element 753 can be made of such birefringent materials as properlyoriented calcite, yttrium orthovanadate (YVO₄), or a-BBO, such as thoseoffered for sale by MT-Optics of Fuzhou, Fujian, China. Birefringentbeam displacement element 753 operates to split an incoming beam 754into a corresponding pair of outgoing beams 755 a and 755 b. As such,beams 755 a and 755 b contain respective light of two orthogonalpolarization states of incoming beam 754. To prepare beams 755 a and 755b for coupling to parallel-aligned (as opposed to orthogonally-oriented)vertical grating couplers in array 230, beam 755 b is passed through ahalf-wave plate 756 to rotate the polarization of light therein. Pasthalf-wave plate 756, beams 755 a and 755 b have the same polarizationstate and, as such, are properly conditioned to use parallel-orientedvertical grating couplers in array 230.

In an alternative embodiment, beam 755 a (instead of beam 755 b) can bepassed through half-wave plate 756 to rotate the polarization of lighttherein. In various embodiments, half-wave plate 756 can be made, e.g.,from quartz crystals, polymer retarder film, or can be 3D printed. Insome embodiments, polarization-diversity structure 757 can bemanufactured using wafer-scale optical processing and assembly.

In some embodiments, polarization-diversity structure 757 can beinserted at other places within connector elements 240 or 250 infiber-to-PIC array connector arrangement 700, e.g., between lenses 741and lenses 742 or between lenses 551 and lenses 541.

In some embodiments, some elements of polarization-diversity structure757 can be functionally split and placed at different locations withinconnector elements 271 and 272. For example, birefringent beamdisplacement element 753 can be placed between fiber end face plane 243and lenses 551, and half-wave plates 756 can be placed between lenses541 and lenses 542.

FIG. 8B shows the schematic side-view 820 of a sub-element ofpolarization-diversity assembly 757 according to an alternativeembodiment. This particular embodiment uses a polarization-sensitivegrating 853, such as offered for sale by ImagineOptix of Durham, N.C.,USA, that operates to split incident light beam 754 into two circularlypolarized beams 855 a and 855 b whose polarizations are mutuallyorthogonal. Beams 855 a and 855 b are directed through an optical layer858 that has a sufficient thickness to have the beams sufficientlylaterally separated. A second polarization grating 859 then operates todiffract the laterally separated beams 855 a and 855 b such that thebeams so diffracted become parallel to the original light beam 754. Asubsequent optical layer 860 comprising a quarter-wave polarizationretarder element 861 and a three-quarter-wave polarization retarderelement 862 then converts the polarizations of both beams 855 a and 855b to the same linear polarization state. In an example embodiment, thislinear polarization state is a proper polarization state for achievingefficient optical coupling of the linearly polarized beams 755 a and 755b into vertical grating couplers of array 230.

The physical principle of the polarization-diversity structure 757 canbe explained as follows. FIGS. 8C to 8E include diagrams that show anincoming beam 830 being split into two polarized beams by thepolarization-diversity structure 757. For example, the incoming beam 830includes two orthogonally polarized components that are spatially splitby a walk-off crystal 832 into a first polarized component 834 and asecond polarized component 836. Referring to FIG. 8C, the incoming beam830 can have polarization components with arbitrary directions, and thewalk-off crystal 832 separates the polarization components into a firstpolarized component 834 and a second polarized component 836 havingpolarizations that are orthogonal to each other and separated by adistanced. As shown in FIGS. 8D and 8E, the component 834 having apolarization direction perpendicular to the plane of the figure passesstraight through the walk-off crystal 832, whereas the component 836having a polarization direction parallel to the plane of the figure isdisplaced by a distance d relative to the component 834.

At least one of the two spatially separated polarization components 834,836 is then rotated by a half-wave plate 838 such that the resultingpolarizations of the two spatial paths are the same. In the example ofFIG. 8D, the polarization of the second polarized component 836 isrotated 90° to generate a polarized component 840 such that thepolarized components 834 and 840 have the same polarization. In theexample of FIG. 8E, the polarization of the first polarized component834 is rotated 90° to generate a polarized component 842 such that thepolarized components 836 and 842 have the same polarization. The twospatially demultiplexed polarization components (834 and 840) or (836and 842) are then incident on a polarization-sensitive vertical gratingcoupler, such as 231 in FIG. 2, to couple into a photonic integratedcircuit, such as 210. In some examples, the grating coupler onlyresponds to either TE (transverse electric) or TM (transverse magnetic)polarization. TE polarized light is characterized by its electric fieldbeing perpendicular to the plane of incidence. For TE light, themagnetic field, which is perpendicular to the electric field inisotropic materials, lies in the plane of incidence.

In some implementations, the fiber-to-PIC arrangement providespolarization management of two orthogonal polarizations between fiber(s)and polarization-dependent PIC coupling element(s), which can bevertical-coupling or edge-coupling elements that respond to, e.g.,circular polarizations, linear polarizations, or any other polarizationstates. The examples described below use photonic integrated circuitedge-coupling elements that respond to a given linear polarization,e.g., vertical grating couplers.

In the example of FIG. 8A, both the birefringent beam displacementelement 753 and the half-wave plate 756 are positioned between the fiberend face plane 243 and the connector mating plane 241. In the someimplementations, the birefringent beam displacement element 753 can bepositioned between the fiber end face plane 243 and the connector matingplane 241, and the half-wave plate 756 can be positioned between theconnector mating plane 241 and the coupling plane 242.

Referring to FIG. 9, in some implementations, a fiber-to-PIC connector900 includes a polarization-diversity structure 902 that includes awalk-off element 904 and a spatially varying birefringent element 906,The walk-off element 904 is positioned between the collimating lens 551and the connector mating plane 241. The spatially varying birefringentelement 906 is positioned between the individual lens 542 and thecoupling plane 242. For example, an incoming beam 908 from a core 302passes the collimating lens 551 and is split by the walk-off element 904into a pair of beams 755 a and 755 b. The polarization of the beam 755 ais orthogonal to the polarization of the beam 755 b. The beam 755 apasses the spatially varying birefringent element 906, which rotates thepolarization direction of the beam 755 a to be the same as thepolarization direction of the beam 755 b. The two beams 755 a and 755 bare then coupled through the vertical-coupling elements 231 to thephotonic integrated circuit 210.

In some implementations, the spatially varying birefringent element 906or the beam displacement element 753 of FIGS. 7 and 8A can be replacedby a birefringent hole plate (BHP) in which a plate of birefringentmaterial includes openings or holes such that light beams can passthrough the holes without any change in the polarization direction,whereas the polarization direction of the light beams that pass throughthe birefringent material are rotated, e.g., by 90°. The birefringenthole plate can be used in combination with a walk-off element such thata light beam is split by the walk-off element into a first polarizationcomponent and a second polarization component, the first polarizationcomponent is directed through the hole in the birefringent hole plate,and the second polarization component is directed through thebirefringent material, thereby producing two polarized beams that havethe same polarization direction.

FIGS. 10A to 10D show various views of a fiber-to-PIC connector 1000 orportions thereof. Referring to FIG. 10A, in some implementations, thefiber-to-PIC connector 1000 is configured to optically couple a row ofincoming beams 1008 from a row of input fiber cores 302. Thefiber-to-PIC connector 1000 includes a polarization-diversity assembly1002 that includes a walk-off crystal 1004 and a birefringent hole plate1006. The birefringent hole plate 1006 has birefringent material atlocations 101 ₂ that function as the half-wave plate 756 of FIGS. 7 and8A. An incoming beam 1008 is split by the walk-off crystal 1004 into twobeams 755 a and 755 b that initially have different polarization states(e.g., orthogonally polarized states). One of the two beams 755 a and755 b is rotated by the birefringent material in the birefringent holeplate 1006 after which the two beams 755 a and 755 b have the samepolarization state.

FIG. 10B is a side view diagram of the fiber-to-PIC connector 1000viewed in a direction A. The incoming light beam 1008 from the core 302passes a collimating lens 551. The walk-off crystal 1004 splits theincoming beam 1008 into two beam components, and the birefringent holeplate 1006 rotates the polarization direction of one of the beamcomponents, resulting in two light beams having the same polarizationstate. The beams pass the second lens 541 and the third lens 542, andare directed to vertical coupling elements 231 on the photonicintegrated circuit 210.

FIG. 10C is a top view of an example of the polarization-diversityassembly 1002 that includes the walk-off crystal 1004 and thebirefringent hole plate 1006, which has a hole 1020. The walk-offcrystal 1004 causes a polarization split resulting in a beamdisplacement in the direction A (the direction A is shown in FIG. 10A),which in this example is parallel to the row direction. The incominglight beam from the core 302 has a polarization component that isdisplaced by the walk-off crystal 1004 from an initial location 1014 toa second location 101 ₆, in which the displacement direction is parallelto the row direction. The dash line 1018 a represents the locations of aset of the second lens 541 and the third lens 542. The dash line 1018 brepresents another set of the second lens 541 and the third lens 542.The centers of the second lens 541 and the third lens 542 are offsetfrom the center of the polarized beam components, which cause thepolarized beam components to be refracted by the lenses and directedtoward the vertical grating couplers at an incident angle θ in a rangebetween 0 to 90°.

FIG. 10D is a top view of another example of the polarization-diversityassembly 1002 in which the polarization split causes a beam displacementperpendicular to the direction A (the direction A is shown in FIG. 10A).In this example, the beam displacement direction is perpendicular to therow direction. The incoming light beam from the core 302 has apolarization component that is displaced by the walk-off crystal 1004from an initial location 1014 to a second location 1022, in which thedisplacement direction is perpendicular to the row direction. Each ofthe dash lines 1018 a and 1018 c represents a set of the second lens 541and the third lens 542. The centers of the second lens 541 and the thirdlens 542 are offset from the center of the polarized beam components,which cause the polarized beam components to be refracted by the lensesand directed toward the vertical grating coupler at an incident angle θin a range between 0 to 90°.

FIG. 11A is a top view of an example of a fiber-to-PIC connector 1100 inwhich a row of four pairs of fiber cores 302 are aligned with four pairsof holes 1020 of a birefringent hole plate 1006. FIG. 11B is a diagramshowing an example in which the walk-off crystal 1004 displaces apolarization component of each bean in a direction 1022 parallel to therow direction. FIG. 11C is a diagram showing an example in which thewalk-off crystal 1004 displaces a polarization component of each bean ina direction 1024 perpendicular to the row direction. The walk-offcrystal can be designed to displace the polarization component of eachbeam in any predetermined direction.

In some implementations, a birefringent plate can have regions withdifferent thicknesses such that when the two polarization componentsprovided by the walk-off element pass two regions with differentthicknesses, the resulting beams have the same polarization direction.For example, if a half-wave plate has a thickness d1, the two regionscan have a difference in thickness equal to d1. A birefringent plate canhave pairs of regions in which each pair includes a first region havinga thickness of d1+d2 and a second region having a thickness of d2. Thetwo orthogonally polarized beam components from the walk-off element aredirected to the pair of regions, in which the polarization of one beamcomponent is rotated 90° relative to the other beam component, resultingin two polarized beams having the same polarization direction.

FIG. 12 is a diagram of an example of the fiber-to-PIC connector 1000 inwhich half-wave plates (e.g., 756) are implemented as a birefringentplate 1006 made of a birefringent material 1200, in which thebirefringent plate 1006 includes areas that does not have birefringentmaterial, i.e., having holes 1020. An incoming light beam 1008 from aninput fiber core 302 is split by the walk-off element 1004 into a firstbeam component 1026 that has “x” polarization and a second beamcomponent 1028 that has “y” polarization. The figure shows an example inwhich the “x” polarization is TE polarization and the “y” polarizationis TM polarization. The first beam component 1026 passes the hole 1020in the birefringent plate 1006 and maintains its polarization. Thesecond beam component 1028 passes the birefringent material 1200 and itspolarization is changed from “y” polarization to “x” polarization. Thefirst and second beam components 1026 and 1028 having the same orparallel polarization then incident upon the grating couplers 231 a and231 b, respectively. The grating couplers 231 a and 231 b couple thefirst and second beam components 1026, 1028 to the photonic integratedcircuit 210. In general, the “hole” plate 1006 has a spatially-varyingbirefringence configured to transform the incident polarized light intothe grating coupler polarization state, e.g., having the polarizationstate that maximizes the coupling efficiency of the grating coupler.

The fiber-to-PIC connector 1000 can combine two output optical signalsfrom the photonic integrated circuit 210 into an output beam that istransmitted on an output fiber core. For example, the photonicintegrated circuit 210 outputs two optical signals that are converted tolight beams 1030 and 1032 through grating couplers 231 c and 231 d,respectively, in which the light beams 1030 and 1032 have the samepolarization state. The light beam 1030 passes the third lens 542 andthe second lens 541, then through a hole 1020 in the birefringent holeplate 1006. The light beam 1030 passes straight through the walk-offelement 1004 without changing direction. The light beam 1032 passes thethird lens 542 and the second lens 541, then through the birefringentmaterial 1200 in the birefringent hole plate 1006, which rotates thepolarization direction of the light beam 1032 by 90°. The light beam1032 is displaced a distance by the walk-off element 1004 and iscombined with the light beam 1030. The combined light beam passes thecollimating lens 551 and is directed to an output fiber core 1034.

FIGS. 13A to 13D are diagrams showing the relationships between anoptical fiber connector, a birefringent hole plate, and gratingcouplers. FIG. 13A is a diagram of a fiber-to-PIC connector 1000, whichis the same as that shown in FIG. 10A. FIG. 13B is a diagram of anoptical fiber connector 1300 that includes transmitter fiber ports(e.g., 1302), receiver fiber ports (e.g., 1304), and optical powersupply fiber ports (e.g., 1306). The circles indicate input fiberlocations (e.g., 302). This example includes 3 rows of 12 fibers. Forexample, the rows can be spaced apart by 500 μm, and the fibers within arow can be spaced apart by 250 μm. In this example, the orange circles(e.g., 1302) represent the transmitter (TX) fiber ports, the browncircles (e.g., 1304) represent the receiver (RX) fiber ports, and thered circles (e.g., 1306) represent the optical power supply fiber ports.Additional information about optical fiber connectors is provided inU.S. provisional patent application 63/145,368, filed on Feb. 3, 2021,the entire contents of which are incorporated by reference.

FIG. 13C is a top view of an example of the birefringent hole plate 1006having holes 1020. The holes 1020 are at the locations of the beams 755a. The walk-off direction is represented by an arrow 1308.

FIG. 13D is a top view of an example of an array of six rows of twelvegrating couplers 1310 (231 in FIGS. 2, 5-7) mounted on top of thephotonic integrated circuit. Each grating coupler 1310 is a TE coupler,in which the direction of the electric field is represented by an arrow1312. The walk-off crystal 1004 splits each input beam into two beamcomponents having orthogonal polarization states, and the birefringenthole plate 1006 rotates the polarization direction of one of the twobeam components such that the two beam components have the samepolarization state upon reaching the grating couplers 1310. Orangetriangles (e.g., 1316) represent the grating couplers for the transmit(TX) signals that are output through the transmitter (TX) fiber ports1302. If the transmit signal has a single polarization, only one gratingcoupler is needed for the corresponding transmitter (TX) fiber port1302. Brown triangles (e.g., 1318) represent the grating couplers forthe receive (RX) signals. Two grating couplers 1310 are needed for eachcorresponding receiver (RX) fiber port 1304 due to random polarizationof the input signals. Red triangles (e.g., 1320) represent the gratingcouplers that correspond to the optical power supply fiber ports 1306.White triangles 1314 indicate that (i) grating couplers are not presentat those locations, (ii) grating couplers are present at those locationsbut not coupled to receive or transmit optical signals, or (iii) gratingcouplers are connected to alignment waveguides to assist with alignmentcalibration.

FIGS. 14A to 18B illustrate examples of grating coupler orientationsthat can be used with the same fiber array show in FIG. 13B. In each ofthese examples, the grating couplers are of the same type, e.g., all TEgrating couplers or all TM grating couplers, and the grating couplersare aligned in the same direction. FIGS. 14A to 18B show examples for TEgrating couplers. The same principles can be applied to TM gratingcouplers with a properly adjusted birefringent hole plate.

FIGS. 14A and 14B illustrate an example of an arrangement of gratingcouplers 1400 and a corresponding birefringent hole plate 1402 thatincludes holes 1404 at predefined locations. This example assumes thatthe walk-off element outputs optical beams with the electric field in adirection 1406. Each input optical beam is split by the walk-off elementinto a first beam component and a second beam component. The first beamcomponent passes straight through the walk-off element, and the secondbeam component is displaced a distance from the first beam componentalong a walk-off direction 1408. The first beam component has electricfield in the direction 1406, which is aligned with the grating coupler.The holes 1404 are positioned to allow the first beam components to passthrough without affecting the polarization states. In this example, thegrating couplers 1400 are oriented to maximize coupling of optical beamswith the electric field in the direction 1406,

FIGS. 15A and 15B illustrate an example of an arrangement of gratingcouplers 1500 and a corresponding birefringent hole plate 1502 thatincludes holes 1504 at predefined locations. This example assumes thatthe walk-off element outputs optical beams with the electric fieldperpendicular to a direction 1506. Each input optical beam is split bythe walk-off element into a first beam component and a second beamcomponent. The first beam component passes straight through the walk-offelement, and the second beam component is displaced a distance from thefirst beam component along a walk-off direction 1508. The second beamcomponent has electric field in the direction 1506, which is alignedwith the grating coupler. The holes 1504 are positioned to allow thesecond beam components to pass through without affecting thepolarization states. In this example, the grating couplers 1500 areoriented to maximize coupling of optical beams with the electric fieldin the direction 1506,

FIGS. 16A and 16B illustrate an example of an arrangement of gratingcouplers 1600 and a corresponding birefringent hole plate 1602 thatincludes holes 1604 at predefined locations. This example assumes thatthe walk-off element outputs optical beams with the electric fieldperpendicular to a direction 1606. Each input optical beam is split bythe walk-off element into a first beam component and a second beamcomponent. The first beam component passes straight through the walk-offelement, and the second beam component is displaced a distance from thefirst beam component along a walk-off direction 1608. The second beamcomponent has electric field in the direction 1606, which is alignedwith the grating coupler. The holes 1604 are positioned to allow thesecond beam components to pass through without affecting thepolarization states. In this example, the grating couplers 1600 areoriented to maximize coupling of optical beams with the electric fieldin the direction 1606,

FIGS. 17A and 17B illustrate an example of an arrangement of gratingcouplers 1700 and a corresponding birefringent hole plate 1702 thatincludes holes 1704 at predefined locations. This example assumes thatthe walk-off element outputs optical beams with the electric fieldparallel to a direction 1706. Each input optical beam is split by thewalk-off element into a first beam component and a second beamcomponent. The first beam component passes straight through the walk-offelement, and the second beam component is displaced a distance from thefirst beam component along a walk-off direction 1708. The first beamcomponent has electric field in the direction 1706, which is alignedwith the grating coupler. The holes 1704 are positioned to allow thefirst beam components to pass through without affecting the polarizationstates. In this example, the grating couplers 1700 are oriented tomaximize coupling of optical beams with the electric field in thedirection 1706,

FIGS. 18A and 18B illustrate an example of an arrangement of gratingcouplers 1800 and a corresponding birefringent hole plate 1802 thatincludes holes 1804 at predefined locations. This example assumes thatthe walk-off element outputs optical beams with the electric fieldperpendicular to a direction 1806. Each input optical beam is split bythe walk-off element into a first beam component and a second beamcomponent. The first beam component passes straight through the walk-offelement, and the second beam component is displaced a distance from thefirst beam component along a walk-off direction 1808. The second beamcomponent has electric field in the direction 1806, which is alignedwith the grating coupler. The holes 1804 are positioned to allow thesecond beam components to pass through without affecting thepolarization states. In this example, the grating couplers 1800 areoriented to maximize coupling of optical beams with the electric fieldin the direction 1806,

FIGS. 13A to 13D, 14A, 14B, 15A, 15B, 16A, 16B, 17A, 17B, 18A, and 18Bshow examples of various orientations of grating couplers andcorresponding birefringent hole plates. The orientation of the gratingcouplers can depend on, e.g., the optical waveguide routing layout. Thegrating couplers can have orientations different from the examplesabove. For example, it is possible to select the orientation of thegrating couplers based on a desired optical waveguide layout, thenorient the walk-off element so that the beam components output from thewalk-off element are either parallel or orthogonal to the direction ofelectric field with maximum coupling efficiency by the grating coupler.The birefringent hole plate is designed such that the holes arepositioned at locations where the beam components do not requirerotation of the polarization direction to achieve maximum couplingefficiency of the grating coupler.

FIGS. 19A to 20C illustrate examples of grating coupler orientationsthat can be used with the same fiber array show in FIG. 13B. In theseexamples, some grating couplers are positioned at locations that arealigned in-between the fiber core locations to achieve a higher density.The grating couplers are of the same type, e.g., TE grating couplers orTM grating couplers, and the grating couplers are aligned in the samedirection. FIGS. 19A to 20C show examples for TE grating couplers. Thesame principles can be applied to TM grating couplers with a properlyadjusted birefringent hole plate.

FIGS. 19A to 19C are diagrams of an example of an arrangement of fiberports 1900, a birefringent hole plate 1902 having holes 1910 atpredefined locations, and an arrangement of grating couplers 1904. Thisexample assumes that the walk-off element outputs optical beams with theelectric field perpendicular to a direction 1906. Each input opticalbeam is split by the walk-off element into a first beam component and asecond beam component. The first beam component passes straight throughthe walk-off element, and the second beam component is displaced adistance from the first beam component along a walk-off direction 1908.The second beam component has an electric field in the direction 1906.In this example, the grating couplers 1904 are oriented to maximizecoupling of optical beams with the electric field in the direction 1906,Because the polarization of the second beam component is already alignedwith the grating coupler, the holes 1910 are positioned to allow thesecond beam components to pass through without changing the polarizationstate. FIG. 19A shows an arrangement of three rows of 12 fiber ports1900. The walk-off direction 1908 is parallel to the row direction. Someof the grating couplers are positioned at locations that are alignedin-between the locations of the fiber ports 1900 to achieve a higherdensity. For example, the distance between two adjacent grating couplers1904 can be about half the distance between two adjacent fiber cores ina row.

FIGS. 20A to 20C are diagrams of an example of an arrangement of fiberports 2000, a birefringent hole plate 2002 having holes 2010 atpredefined locations, and an arrangement of grating couplers 2004. Thisexample assumes that the walk-off element outputs optical beams with theelectric field parallel to a direction 2006. Each input optical beam issplit by the walk-off element into a first beam component and a secondbeam component. The first beam component passes straight through thewalk-off element, and the second beam component is displaced a distancefrom the first beam component along a walk-off direction 2008. The firstbeam component has electric field in the direction 2006. In thisexample, the grating couplers 2004 are oriented to maximize coupling ofoptical beams with the electric field in the direction 2006, Because thepolarization of the first beam component is already aligned with thegrating coupler, the holes 2010 are positioned to allow the first beamcomponents to pass through without changing the polarization state. FIG.20A shows an arrangement of three rows of 12 fiber ports. The walk-offdirection 2008 is at an angle (e.g., 45°) relative to the row direction.Some of the grating couplers are positioned at locations that arealigned in-between the locations of the fiber ports 2000 to achieve ahigher density. In the example of FIG. 20A, the distance betweenadjacent fiber cores in a row is the same as the distance betweenadjacent fiber cores in a column. For example, the distance between twoadjacent grating couplers 2004 can be about 70% of the distance betweentwo adjacent fiber cores in a row.

Referring to FIGS. 21A to 21D, a birefringent hole plate can have holeshaving one or more of various shapes. FIG. 21A is a diagram of anexample of a birefringent hole plate 2100 that has holes 2102 with acircular shape. FIG. 21B is a diagram of an example of a birefringenthole plate 2104 that has holes 2106 with a square shape. FIG. 21C is adiagram of an example of a birefringent hole plate 2108 that has stripholes 2110. In some examples, the holes can have a rectangular shape.FIG. 21D is a diagram of an example of a birefringent hole plate 2116that includes multiple individual strip platelets 2112 that are spacedapart, in which the space 2114 between the strip platelets 2112 form the“holes” of the birefringent hole plate 2116. In some implementations,the holes of the birefringent hole plate can have a combination ofdifferent shapes, and the shapes can have arbitrary geometries.

In general, micro-optic systems can include multiple optical elements,including optically birefringent elements that are employed to modifythe polarization of light. In some applications, a patternedbirefringent element can have non-uniform birefringence across an areato vary the polarization modification induced by the element. An exampleis a half-wave plate (HWP) in which an array of vias is drilled throughthe element so the polarization of light passing through the vias isunchanged while light passing through the half-wave plate material mayexperience a change in polarization.

In some implementations, a patterned birefringent plate can be generatedby bonding birefringent elements to a second element in the micro-opticsystem in which a pattern is generated in the birefringent elementsafter bonding through processes such as etching, mechanical removal,laser cutting, laser ablation, etc. The patterned birefringent plate hasnon-uniform birefringence across a plane in which light passes throughso that different portions of light pass through different portions ofthe patterned birefringent plate having difference birefringence. Thepatterned birefringent plate can affect an optical property of differentportions of the light differently. So example, the patternedbirefringent plate can rotate the polarization of a first portion oflight by a first amount and rotate the polarization of a second portionof light by a second amount.

Another approach to generating a patterned birefringent plate havingpatterns in the birefringent material is to modify the birefringence ofthe birefringent element with no or minimal removal of material. Anexample is using local laser heating to generate patterns of modifiedbirefringence in a material such as crystalline quartz. Heating ofcrystalline quartz to near its melting point can disrupt the crystallinestructure, producing fused silica which has an amorphous structure withno birefringence. Patterned localized heating to generate regions offused silica within the crystalline quartz can have an effect similar toforming holes or strips in the birefringent hole plates shown in FIGS.21A to 21D. In some examples, one or more particle beams, such aselectron beams, can energize the crystalline quartz to modify itsbirefringence.

FIG. 50 shows a top view 5000 and a side view 5002 of an example of apatterned birefringent plate 5004 in which a patterned birefringentelement is attached to a second element. The patterned birefringentplate 5004 has non-uniform birefringence across a plane parallel to thetop surface of the patterned birefringent plate 5004, and exhibitsnon-uniform birefringence properties with respect to light that passesthrough the patterned birefringent plate 5004 by entering the top side5006 (or the bottom side 5008) and exiting the bottom side 5008 (or thetop side 5006) of the patterned birefringent plate 5004.

In some implementations, an optically birefringent element 5010 isbonded to a second optical element 5012, and a pattern is formed in theoptically birefringent element 5010. In some implementations, a patternis formed in the optically birefringent element 5010 first, then thepatterned optically birefringent element 5010 is bonded to the secondoptical element 5012. In the example shown in FIG. 50, the patternedbirefringent element 5010 can be generated by the removal ofbirefringent material. This removal can be achieved by a variety ofmethods including, e.g., mechanical removal, laser ablation, andetching. The etching can be, e.g., liquid-phase etching (also referredto as wet chemical etching) or plasma-phase etching (also referred to asdry etching). The removal process can be controlled to prevent removalof material from the second optical element 5012, for example, by usingan etch stop layer at the interface between the birefringent material5010 and the second element 5012. For example, the etch stop layer canbe an anti-reflective coating that enhances the transmission of lightbetween the birefringent material 5010 and the second optical element5012, in which the anti-reflective coating is also resistant to theetching.

In some implementations, the use of a chemical etching process to removethe birefringent material instead of using mechanical drilling togenerate openings in the birefringent material has the advantage thatthe patterned birefringent element 5010 thus produced is relativelyclean without significant debris that may occur when mechanical drillingis used to generate the openings. This beneficial feature is significantwhen the patterns in the birefringent element 5010 has small dimensions.In the example shown in FIG. 50, the patterned optically birefringentelement 5010 includes a plurality of strips of birefringent material5014 extending parallel to one another. In the regions between thestrips of birefringent material 5014, the birefringent material has beenetched away.

In some implementations, the width d1 of each strip of birefringentmaterial 5014 is substantially equal to the width d2 of the etchedregion 5016 between the strips of birefringent material 5014. The widthsd1 and d2 are selected to be slightly larger than the diameter of thelight beams that pass through the strip of birefringent material 5014and the etched region 5016. In some examples, the width d1 can also bedifferent from the width d2.

For example, a light beam from an optical fiber core can be split by abirefringent beam displacement element, walk-off element,polarization-sensitive grating (e.g., 753 of FIGS. 7 and 8A, 853 of FIG.8B, 832 of FIGS. 8C to 8E, 904 of FIG. 9, 1004 of FIGS. 10A to 10C, 12,and 13A, 2306 of FIG. 23, 2408 of FIG. 24A, 2906 of FIG. 29, 3008 ofFIG. 30, 3400 of FIGS. 34A and 34B, 3512 of FIG. 35, 3908 of FIG. 39,4002 of FIG. 40) into a first beam component 5018 (e.g., similar to 834or 2308) and a second beam component 5020 (e.g., similar to 836 or2310), in which the first and second beam components 5018, 5020 areseparated in the walk-off direction 5022. The walk-off element can bedesigned such that after exiting the walk-off element, the first beamcomponent 5018 has a polarization that is orthogonal to the polarizationof the second beam component 5020. The walk-off element directs thefirst beam component 5018 towards the etched region 5016, and directsthe second beam component 5020 towards the strip of birefringentmaterial 5014. The strip of birefringent material 5014 changes thepolarization of the second beam component 5020, while the first beamcomponent 5018 passes through the etched region 5016 without any changein polarization. The thickness of the patterned optically birefringentelement 5010 can be selected such that the patterned opticallybirefringent element 5010 is functionally equivalent to a half-waveplate having openings at the etched regions 5016. In this example, thepolarization of the second beam component 5020 is rotated 90°+n×180°,0≤n, n being an integer. After passing the patterned opticallybirefringent element 5010, the polarization of the first beam component5018 becomes parallel to the polarization of the second beam component5020.

The birefringent beam displacement element, walk-off element, orpolarization-sensitive grating can also be used as a beam combiner tocombine the beam components emitted from the vertical coupling elementsand passed through the patterned optically birefringent element 5010into one light beam that is transmitted to a corresponding optical fibercore.

In the example of FIG. 50, the birefringent material is completelyetched away in the etched region 5016. In some implementations, thebirefringent material is partially etched, such that the polarization ofthe first beam component 5018 is also rotated by the remainingbirefringent material in the etched region 5016. The un-etched strip ofbirefringent material 5014 has a greater thickness and the polarizationof the second beam component 5020 is rotated by a greater amount. Thedepth of the etching can be selected such that the polarization of thesecond beam component 5020 is rotated 90°+n×180°, 0≤n, n being aninteger, relative to the polarization of the first beam component 5018.

In some implementations, the light beams from the optical fiber coresupon reaching the patterned optically birefringent element 5010 can havea diameter in a range from 49 μm to 999 μm, and the width d1 of eachstrip of birefringent material 5014 and the width d2 of the etchedregion 5016 can be in a range from 50 μm to 1000 μm. In some examples,the light beams from the optical fiber cores upon reaching the patternedoptically birefringent element 5010 can have a diameter in a range from99 μm to 599 μm, and the width d1 of each strip of birefringent material5014 and the width d2 of the etched region 5016 can be in a range from100 μm to 600 μm. In some examples, the light beams from the opticalfiber cores upon reaching the patterned optically birefringent element5010 can have a diameter in a range from 199 μm to 399 μm, and the widthd1 of each strip of birefringent material 5014 and the width d2 of theetched region 5016 can be in a range from 200 μm to 400 μm.

The arrangement of the parallel strips of birefringent material 5014 andthe etched regions 5016 correspond to the arrangement of the opticalfibers that are coupled to the fiber-optic connector. For example, theoptical fibers can be arranged in a two-dimensional array having atleast 2 rows and at least 8 columns. The etched regions can include atleast 2 parallel strips of etched regions. The patterned opticallybirefringent element 5010 shown in FIG. 50 includes 3 parallel strips ofbirefringent material 5014 and can be used in a fiber-optic connectorfor coupling an array of 3 rows of optical fibers to a correspondingarray of vertical coupling elements on the photonic integrated circuit.

In some implementations, the etched regions can have a shapesubstantially resembling a circle, an oval, a triangle, a square, arectangle, or a polygon having n sides, n being an integer greater than4, and the shape is measured along a plane parallel to the top surfaceof the second optical element 5012. In this example, the size of theetched regions are selected to be slightly larger than the size of thelight beams. For example, each of the etched region can have a dimensionmeasured along a direction parallel to the walk-off direction in a rangefrom 50 μm to 1000 μm. For example, each of the etched region can have adimension measured along a direction parallel to the walk-off directionin a range from 100 μm to 600 μm. For example, each of the etched regioncan have a dimension measured along a direction parallel to the walk-offdirection in a range from 20 μm to 400 μm.

The arrangement of the etched regions correspond to the arrangement ofthe optical fibers that is coupled to the fiber-optic connector. Forexample, the optical fibers can be arranged in a two-dimensional arrayhaving at least 2 rows and at least 8 columns. In this example, theetched regions can also be arranged in a two-dimensional array having atleast 2 rows and at least 8 columns.

The dimensions for the etched regions or strips of birefringent materialare provided as examples only. It is understood that the etch regionsand the strips of birefringent material can have larger dimensions,e.g., when larger optical fiber cores are used, when the optical fibercores are spaced farther apart from one another, and/or when thevertical coupling elements are spaced farther apart from one another.

The half-wave plate or birefringent hole plate of FIGS. 7, 9, 10A, 11A,111B, 11C, 12, 13A, 13C, 14B, 15B, 16B, 17 b, 18B, 19B, 20B, 21A-21D,23, 28, 29, 30, 35, 36, 38-40, and 49 can be replaced by a patternedbirefringent plate in which some of the birefringent material is removedby etching, similar to the patterned birefringent plate 5004 of FIG. 50.For example, fabricating the fiber-to-PIC connector 700 includesfabricating the connector element 250. Fabricating the connector element250 includes fabricating a patterned birefringent plate, and attachingthe birefringent plate to another optical element, e.g., an opticalelement that includes the array of collimating lenses 551. Fabricatingthe fiber-to-PIC connector 900 includes fabricating the connectorelement 240. Fabricating the connector element 240 includes fabricatinga patterned birefringent plate, and attaching the birefringent plate toanother optical element, e.g., an optical element that includes thearray of second lenses 541 and the array of third lenses 542.

The fiber-to-PIC connector (e.g., 700, 900) will also be referred to asa fiber-optic connector, and the connector element (e.g., 240, 250) willalso be referred to as a fiber-optic connector part. Thus, in someimplementations, fabricating a fiber-optic connector includes generatinga patterned birefringent plate by attaching a birefringent element to asecond optical element, and applying a removal process (e.g., etchingprocess) to remove portions of the optically birefringent material at aplurality of first regions such that after the removal process theplurality of first regions have no optically birefringent material orhave optically birefringent material with reduced thickness. Fabricatingthe fiber-optic connector further includes attaching the patternedbirefringent plate to another connector part (e.g., a connector partthat includes the array of collimating lenses 551 or the array of secondlenses 541 and the array of third lenses 542).

FIG. 51 shows a top view 5100 and a side view 5102 of an example of apatterned birefringent plate 5104 in which a patterned opticallybirefringent element 5110 is attached to a second optical element 5112.The birefringent plate 5104 has non-uniform birefringence across a planeparallel to the top surface of the birefringent plate 5104, and exhibitsnon-uniform birefringence properties with respect to light that passesthrough the birefringent plate 5104 by entering the top side 5106 (orthe bottom side 5108) and exiting the bottom side 5108 (or the top side5106) of the birefringent plate 5104.

In some implementations, an optically birefringent element 5110 withoutpattern is bonded to the second optical element 5112, and the pattern isgenerated in the optically birefringent element 5110 after bonding tothe second optical element 5112. In some implementations, a pattern isformed in the optically birefringent element 5110 to produce a patternedoptically birefringent element 5110, and the patterned opticallybirefringent element 5110 is bonded to the second optical element 5112.The patterns are selected for specific applications, in which thepatterns can include the degree and orientation of the opticalbirefringence varying across the patterned optically birefringentelement 5110.

In some implementations, a birefringent pattern can be generated bylocalized heating of a birefringent material to modify the materialproperties, resulting in altered, reduced or substantially nobirefringence. Either no material is removed in the localized heatingprocess, or only a small amount of material is removed in the localizedheating process. For example, localized laser heating can be applied tocrystalline quartz (which has a birefringence property) to produce areasof amorphous fused silica having modified, low, or substantially nobirefringence. In some examples, the laser is sequentially applied tothe various regions one after another to sequentially produce the areashaving lower birefringence. In some examples, multiple laser beams(e.g., by using multiple laser sources or splitting each of one or morelaser beams into multiple beams) are applied to the various regions inparallel to produce the areas having lower birefringence in parallel.

Here, a material is considered to have substantially no birefringence ifit rotates the polarization of light by, e.g., less than 5°, or in someexamples less than 1°. For example, the inverse process can also be usedin which localized heating of a non-birefringent material can generateregions of birefringence.

In the example of FIG. 51, the localized heating is applied to firstregions 5112 (in the shape of parallel strips) of the opticallybirefringent element 5110 to cause the first regions 5112 to havereduced or substantially no birefringence. After the localized heating,the optically birefringent element 5110 has a striped pattern thatincludes first regions 5112 alternating with second regions 5114, inwhich the first regions 5112 include parallel strips of material havinglow or no birefringence, and the second regions 5114 include parallelstrips of the birefringent material that maintains its birefringence.

In some implementations, the use of localized heating to reduce thebirefringence of the material instead of using mechanical drilling togenerate openings in the birefringent material has the advantage thatthe patterned birefringent element thus produced is relatively cleanwithout significant debris that may occur when mechanical drilling isused to generate the openings. This beneficial feature is significantwhen the patterns in the birefringent element 5110 has small dimensions.In the example shown in FIG. 51, the patterned optically birefringentelement 5110 includes a plurality of strips of birefringent material5114 extending parallel to one another. In the regions 5112 between thestrips of birefringent material 5114, localized heating has been appliedto reduce the birefringence, e.g., to substantially no birefringence.

In some implementations, the width d3 of each strip of material havingreduced or no birefringence in the first regions 5112 is substantiallyequal to the width d4 of the strip of birefringent material in thesecond regions 5114. The widths d3 and d4 are selected to be slightlylarger than the diameter of the light beams that pass through the stripin the first region 5112 and the strip in the second region 5114. Insome examples, the width d3 is different from the width d4.

For example, a light beam from an optical fiber core can be split by abirefringent beam displacement element, walk-off element, orpolarization-sensitive grating (e.g., 753 of FIGS. 7 and 8A, 853 of FIG.8B, 832 of FIGS. 8C to 8E, 904 of FIG. 9, 1004 of FIGS. 10A to 10C, 12,and 13A, 2306 of FIG. 23, 2408 of FIG. 24A, 2906 of FIG. 29, 3008 ofFIG. 30, 3400 of FIGS. 34A and 34B, 3512 of FIG. 35, 3908 of FIG. 39,4002 of FIG. 40) into a first beam component 5118 (e.g., similar to 834or 2308) and a second beam component 5120 (e.g., similar to 836 or2310), in which the first and second beam components 5118, 5120 areseparated in the walk-off direction 5122. The walk-off element can bedesigned such that after exiting the walk-off element, the first beamcomponent 5118 has a polarization that is orthogonal to the polarizationof the second beam component 5120. The walk-off element directs thefirst beam component 5118 towards the first region 5112 having reducedor substantially no birefringence, and directs the second beam component5120 towards the second region 5114 that maintains its birefringentproperty. The birefringent material in the second region 5114 changesthe polarization of the second beam component 5120 by a first amount,while the first beam component 5018 passes through the first region 5112without any change in polarization (if the first region 5112 hassubstantially no birefringence) or with a smaller amount of change inpolarization (if the first region 5112 has reduced birefringence). Thethickness of the patterned optically birefringent element 5110 and thethickness of the first region 5112 that is subject to localized heatingcan be selected such that the patterned optically birefringent element5110 is functionally equivalent to a half-wave plate having openings atthe first regions 5110. In this example, the polarization of the secondbeam component 5120 is rotated 90°+n×180°, 0≤n, n being an integerrelative to the polarization of the first beam component 5118. Afterpassing the patterned optically birefringent element 5110, thepolarization of the first beam component 5118 becomes parallel to thepolarization of the second beam component 5120.

The birefringent beam displacement element, walk-off element, orpolarization-sensitive grating can also be used as a beam combiner tocombine the beam components emitted from the vertical coupling elementsand passed through the patterned optically birefringent element 5110into one light beam that is transmitted to a corresponding optical fibercore.

In some implementations, the light beams from the optical fiber coresupon reaching the patterned optically birefringent element 5110 can bein a range from 49 μm to 999 μm, and the width d4 of each strip ofbirefringent material in the second region 5114 and the width d3 of thestrip of material having reduced or substantially no birefringence inthe first region 5112 can be in a range from 50 μm to 1000 μm. In someexamples, the light beams from the optical fiber cores upon reaching thepatterned optically birefringent element 5110 can be in a range from 99μm to 599 μm, and the width d4 of each strip of birefringent material inthe second region 5114 and the width d3 of the strip of material havingreduced or substantially no birefringence in the first region 5112 canbe in a range from 100 μm to 600 μm. In some examples, the light beamsfrom the optical fiber cores upon reaching the patterned opticallybirefringent element 5010 can be in a range from 199 μm to 399 μm, andthe width d4 of each strip of birefringent material in the second region5114 and the width d3 of the strip of material having reduced orsubstantially no birefringence in the first region 5112 can be in arange from 200 μm to 400 μm.

The arrangement of the parallel strips of birefringent material in thesecond regions 5114 and the parallel strips of material having reducedor substantially no birefringence in the first regions 5112 correspondto the arrangement of the optical fibers that are coupled to thefiber-optic connector. For example, the optical fibers can be arrangedin a two-dimensional array having at least 2 rows and at least 8columns. In this example, the locally heated regions, i.e., the firstregions 5112, can include at least 2 parallel strips of material havingreduced or substantially no birefringence. The patterned opticallybirefringent element 5110 shown in FIG. 51 includes 3 parallel strips ofmaterial having reduced or substantially no birefringence and can beused in a fiber-optic connector for coupling an array of 3 rows ofoptical fibers to a corresponding array of vertical coupling elements onthe photonic integrated circuit.

In some implementations, each of the locally heated regions can have ashape substantially resembling a circle, an oval, a triangle, a square,a rectangle, or a polygon having n sides, n being an integer greaterthan 4, and the shape is measured along a plane parallel to the topsurface of the second optical element 5112. In this example, the size ofthe locally heated regions are selected to be slightly larger than thesize of the light beams. For example, each of the locally heated regioncan have a dimension measured along a direction parallel to the walk-offdirection in a range from 50 μm to 1000 μm. For example, each of thelocally heated region can have a dimension measured along a directionparallel to the walk-off direction in a range from 100 μm to 600 μm. Forexample, each of the locally heated region can have a dimension measuredalong a direction parallel to the walk-off direction in a range from 200μm to 400 μm.

The arrangement of the locally heated regions correspond to thearrangement of the optical fibers that is coupled to the fiber-opticconnector. For example, the optical fibers can be arranged in atwo-dimensional array having at least 2 rows and at least 8 columns. Inthis example, the locally heated regions can also be arranged in atwo-dimensional array having at least 2 rows and at least 8 columns.

The dimensions for the locally heated regions or strips resulting inreduced or substantially no birefringence are provided as examples only.It is understood that the etch regions and the strips of birefringentmaterial can have larger dimensions, e.g., when larger optical fibercores are used, when the optical fiber cores are spaced farther apartfrom one another, and/or when the vertical coupling elements are spacedfarther apart from one another.

The half-wave plate or birefringent hole plate of FIGS. 7, 9, 10A, 11A,111B, 11C, 12, 13A, 13C, 14B, 15B, 16B, 17 b, 18B, 19B, 20B, 21A-21D,23, 28, 29, 30, 35, 36, 38-40, and 49 can be replaced by a patternedbirefringent plate in which localized heating is applied to some regionsof the birefringent material to reduce the birefringence, similar to thepatterned birefringent plate 5104 of FIG. 51. For example, fabricatingthe fiber-to-PIC connector 700 includes fabricating the connectorelement 250. Fabricating the connector element 250 includes fabricatinga patterned birefringent plate, and attaching the birefringent plate toanother optical element, e.g., an optical element that includes thearray of collimating lenses 551. For example, fabricating thefiber-to-PIC connector 900 includes fabricating the connector element240. Fabricating the connector element 240 includes fabricating apatterned birefringent plate, and attaching the birefringent plate toanother optical element, e.g., an optical element that includes thearray of second lenses 541 and the array of third lenses 542.

Thus, in some implementations, fabricating a fiber-optic connectorincludes applying localized heating to a birefringent plate to produce apatterned birefringent plate, in which the localized heating modifiesbirefringence of a plurality of first regions in the birefringent plateto cause the first regions to have birefringence that is different fromthe birefringence of second regions that do not receive the localizedheating. Fabricating the fiber-optic connector further includesattaching the patterned birefringent plate to another connector part(e.g., a connector part that includes the array of collimating lenses551 or the array of second lenses 541 and the array of third lenses542).

Referring to FIGS. 52A to 52D, in some implementations, a pattern ofmodified, reduced, or substantially zero birefringence can be generatedwithin the volume of a birefringent element. The inverse is possible inwhich a birefringent pattern is generated within the volume of anon-birefringent element.

FIG. 52A is a perspective view of an example of a patterned birefringentplate 5200 that includes a stripe pattern of modified birefringence. Astrip of material 5202 having reduced or no birefringence is generatedwithin the volume of the patterned birefringent plate 5200.

In some implementations, the modified birefringence pattern can begenerated through the entire thickness of the birefringent element. FIG.52B is a side view of an example of a patterned birefringent plate 5204in which a strip of material 5206 having reduced or no birefringenceextends from a top surface 5208 to a bottom surface 5210 of thepatterned birefringent plate 5204.

In some implementations, the modified birefringence pattern can begenerated inside the volume of the birefringent element. FIG. 52C is aside view of an example of a patterned birefringent plate 5212 in whicha strip of material 5214 having reduced or no birefringence ispositioned within the volume of the patterned birefringent plate 5212 ata first distance from the top surface 5208 and a second distance fromthe bottom surface 5210 of the patterned birefringent plate 5212.

In some implementations, the modified birefringence pattern can begenerated near the surface of the birefringent element. FIG. 52D is aside view of an example of a patterned birefringent plate 5216 in whicha strip of material 5218 having reduced or no birefringence extends froma top surface 5208 to a location at a distance from the bottom surface5210 of the patterned birefringent plate 5216.

The different types of patterns shown in FIGS. 52B to 52D can begenerated by focusing a laser beam at different depths in the volume ofthe birefringent plate to locally heat the birefringent material atdifferent depths. In these examples, the locally heated region (e.g.,5206, 5214, 5218) is an integral portion of the patterned birefringentplate, and no glue or adhesive is used to bond the locally heated regionto other portions of the patterned birefringent plate.

FIGS. 53A and 53B are diagrams showing examples of birefringent platesthat have patterns generated in the birefringent element. FIG. 53A showsan example of a birefringent plate 5300 having parallel stripes 5302patterned in the birefringent element. FIG. 53B shows an example of abirefringent plate 5304 having an array of circles 5306 patterned in thebirefringent element.

FIG. 53C is a diagram showing incident light 5308 passing through apatterned birefringent plate 5310 that includes first regions 5312having a pattern of material with zero birefringence. For example, theincident light 5308 can be either a single wavefront or a pattern ofbeamlets. The polarization of light 5314 is unchanged when passingthrough non-birefringent patterns 5312. The polarization of light 5316is changed when passing through the birefringent material of thebirefringent plate 5310.

In some implementations, a process of fabricating a fiber-opticconnector part (e.g., connector element 250 of FIG. 7 or connectorelement 240 of FIG. 9) includes applying localized heating or localizedenergizing to a birefringent plate (e.g., 5104) to modify birefringenceof a two-dimensional pattern of first regions (e.g., 5112) in thebirefringent plate to cause the first regions to have birefringence thatis different from the birefringence of second regions (e.g., 5114) thatdo not receive the localized heating or localized energizing. Theprocess includes coupling the birefringent plate to a second opticalcomponent (e.g., 5112) to form a fiber-optic connector part that isconfigured to be coupled to at least one of a plurality of opticalfibers or a plurality of vertical coupling elements on a photonicintegrated circuit, and the birefringent plate comprises non-uniformbirefringence properties with respect to light that passes through thebirefringent plate.

For example, the birefringent plate can be configured to modify apolarization state of a first set of light beams (e.g., 5118) that passthrough the first regions of the birefringent plate relative to apolarization state of a second set of light beams (e.g., 5120) that passthrough the second regions of the birefringent plate.

For example, the localized heating or localized energizing can beapplied to the birefringent plate to modify birefringence of atwo-dimensional array of first regions in the birefringent plate tocause the array of first regions to have birefringence that is differentfrom the birefringence of second regions that do not receive thelocalized heating, and the two-dimensional array includes at least 2rows and at least 8 columns.

For example, the spacing between two adjacent rows in thetwo-dimensional array can be identical to the spacing between twoadjacent columns in the two-dimensional array.

For example, the fiber optic connector part can be configured to beoptically coupled to a two-dimensional array of optical fibers.

For example, the fiber optic connector part can be configured to beoptically coupled to a two-dimensional array of vertical couplingelements on the photonic integrated circuit.

For example, the fiber-optic connector part can be configured to enablethe first set of light beams and the second set of light beams to betransmitted between the two-dimensional array of optical fibers and thetwo-dimensional array of vertical coupling elements. The birefringentplate can be configured to modify a polarization state of a first set oflight beams that pass through the first regions of the birefringentplate relative to a polarization state of a second set of light beamsthat pass through the second regions of the birefringent plate.

For example, each of at least some of the first regions can have asubstantially circular, oval, triangular, square, or rectangular shape.

For example, the two-dimensional pattern of first regions can include atleast 2 parallel strips of first regions. Applying localized heating tothe birefringent plate can include applying localized heating to modifybirefringence of the at least 2 parallel strips of first regions in thebirefringent plate to cause the at least 2 parallel strips of firstregions to have birefringence that is different from the birefringenceof the second regions that do not receive the localized heating.

In some examples, each strip of first region has a width in a range from50 μm to 1000 μm. In some examples, each strip of first region has awidth in a range from 100 μm to 600 μm. In some examples, each strip offirst region has a width in a range from 200 μm to 400 μm.

For example, the fiber-optic connector part can be configured to beoptically coupled to a plurality of vertical coupling elements on thephotonic integrated circuit, and the fiber-optic connector is configuredto enable the first set of light beams and the second set of light beamsto be transmitted between the plurality of optical fibers and theplurality of vertical coupling elements.

For example, applying the localized heating or localized energizing tothe birefringent plate can include applying the localized heating orlocalized energizing to the birefringent plate to reduce thebirefringence at the first regions.

For example, applying the localized heating or localized energizing tothe birefringent plate can include applying the localized heating orlocalized energizing to the birefringent plate to reduce thebirefringence at the first regions to substantially zero birefringence.

For example, applying the localized heating or localized energizing tothe birefringent plate can comprises applying the localized heating orlocalized energizing to the birefringent plate to reduce thebirefringence at the first regions such that the second set of lightbeams that pass through the second regions have polarization that isrotated about 90°+n×180°, 0≤n, n being an integer, relative topolarization of the first set of light beams that pass through the firstregions.

For example, the fiber-optic connector part can include a walk-offelement configured to: receive a plurality of light beams from theplurality of optical fibers, split the light beams into first beamcomponents and second beam components, the second beam components havepolarization that is orthogonal to the polarization of the first beamcomponents, direct the first beam components toward the first regionshaving lower birefringence, and direct the second beam components towardthe second regions having higher birefringence.

For example, applying the localized heating or localized energizing tothe birefringent plate can include applying the localized heating orlocalized energizing to the birefringent plate to reduce thebirefringence at the first regions such that the second set of lightbeams that pass through the second regions have polarization that isrotated about 90°+n×180°, 0≤n, n being an integer, relative topolarization of the first set of light beams that pass through the firstregions. The walk-off element can be configured such that upon exitingthe walk-off element the first beam components have a firstpolarization, and the second beam components have a second polarizationthat is substantially orthogonal to the first polarization. The firstand second regions of the birefringent plate can be configured such thatafter passing the first and second regions the first beam componentshave polarization that is substantially parallel to the polarization ofthe second beam components.

For example, the walk-off element can separate the first beam componentand the second beam component along a walk-off direction, each of atleast some of the first regions can have a dimension measured along adirection parallel to the walk-off direction in a range from 50 μm to1000 μm.

For example, each of at least some of the first regions can have adimension measured along a direction parallel to the walk-off directionin a range from 100 μm to 600 μm.

For example, each of at least some of the first regions can have adimension measured along a direction parallel to the walk-off directionin a range from 200 μm to 400 μm.

For example, applying localized heating or localized energizing to thebirefringent plate can include applying localized heating or localizedenergizing to the birefringent plate to modify birefringence of thetwo-dimensional pattern of first regions in the birefringent plate suchthat the birefringent plate is configured to modify polarization oflight passing the birefringent plate in a way that is equivalent tomodification of polarization of light passing a half-wave plate havingopenings at the two-dimensional pattern of first regions.

For example, the birefringent plate includes a first surface and asecond surface. Applying localized heating to the birefringent plate caninclude applying localized heating to first regions that extend from thefirst surface to the second surface. See the example of birefringentplate 5204 in FIG. 52B.

For example, the birefringent plate includes a first surface and asecond surface. Applying localized heating or localized energizing tothe birefringent plate can include applying localized heating orlocalized energizing to first regions that are positioned within thebirefringent plate and spaced at a first distance from the first surfaceand a second distance from the second surface. See the example ofbirefringent plate 5212 in FIG. 52C.

For example, the birefringent plate includes a first surface and asecond surface. Applying localized heating or localized energizing tothe birefringent plate can include applying localized heating orlocalized energizing to first regions that extend from the first surfaceto a location inside the birefringent plate, the first regions arespaced at a distance from the second surface. See the example ofbirefringent plate 5216 in FIG. 52D.

For example, one or more laser beams can be used to apply the localizedheating.

For example, one or more particle beams can be used to apply thelocalized energizing.

During fabrication of the fiber-optic connector part, various opticalcomponents in the fiber-optic connector need to be properly aligned toensure that light beams from the optical fibers can be properlytransmitted to the vertical coupling elements on the photonic integratedcircuit. For example, to fabricate the connector element 250, the arrayof collimating lens 551 needs to be aligned with the polarizationdiversity assembly 757. Aligning the optical components takes time, soit is preferable to manufacture the fiber-optic connector parts in a waythat the time spent on aligning the optical components is reduced.

In some implementations, a process for manufacturing a plurality offiber-optic connector parts includes aligning and bonding multipleoptical components in parallel to form an assembly, then cutting theassembly to singulate the individual fiber-optic connector parts. Forexample, a first substrate having multiple un-singulated first opticalcomponents is aligned and bonded with a second substrate having multipleun-singulated second optical components to form an assembly thatincludes the first substrate and the second substrate. The assembly isthen cut to singulate the individual fiber-optic connector part thatincludes the first and second optical components.

In some implementations, a process for fabricating fiber-optic connectorparts includes: providing a first module having a plurality ofunsingulated lens arrays; and providing a second module having aplurality of unsingulated patterned birefringent plates. Each patternedbirefringent plate includes birefringent material, the patternedbirefringent plate includes a plurality of first regions having reducedor no birefringence as compared to a plurality of second regions. Theprocess includes aligning the plurality of unsingulated lens arrays inthe first module to the plurality of unsingulated patterned birefringentplates in the second module; bonding the first module to the secondmodule to form a first assembly; and cutting the first assembly tosingulate the first and second modules to produce a plurality offiber-optic connector parts. Each fiber-optic connector part comprises asingulated birefringent plate and a singulated lens array.

In some implementations, using similar principles described above, thepatterned birefringent plate can be configured to be equivalent to aquarter-wave plate with holes.

In some implementations, the array of grating couplers can include afirst subset of grating couplers that are used to couple optical signalsbetween the fiber cores and the photonic integrated circuit, and asecond subset of grating couplers that are not used to couple opticalsignals between the fiber cores and the photonic integrated circuit. Thesecond subset of grating couplers can be used for alignment purposes.

Referring to FIG. 22, an array of grating couplers 2200 includestransmit-grating couplers 2202 for coupling output or transmit opticalsignals, receive-grating couplers 2204 for coupling input or receiveoptical signals, and optical power supply-grating couplers 2206 forcoupling optical power supply light. This example assumes a walk-offdirection 2208. The array of grating couplers 2200 includes unusedtransmit-grating couplers, e.g., 2210 a and 2210 b, that can beconnected by waveguides, e.g., 2212, to enable active alignment duringassembly. The term “unused transmit-grating coupler” refers to a gratingcoupler that is not used to couple optical signals between the fibersand the photonic integrated circuit. For example, the “unusedtransmit-grating coupler is positioned adjacent to anothertransmit-grating coupler, in which the unused transmit-grating coupleris displaced from the second transmit-grating coupler along the walk-offdirection.

The photonic integrated circuit can be designed such that a light signalis output from the photonic integrated circuit to the grating coupler2210 a, and a photodetector detects light received from the gratingcoupler 2210 b. During assembly of the photonic integrated circuit withthe fiber-to-PIC connector, the light received from the grating coupler2210 b is monitored to optimize alignment of the fiber-to-PIC connectorto the photonic integrated circuit, e.g., by finding an alignmentbetween the photonic integrated circuit and the fiber-to-PIC connectorthat achieves the highest efficiency of light transfer from the lightoutput port of the photonic integrated circuit to the grating coupler2210 a and from the grating coupler 2210 b to the photodetector.

By using the unused transmit-grating couplers within the array ofgrating couplers for alignment purposes, there is no need to increasethe overall footprint of the array of grating couplers. The geometricsize of the array of grating couplers can be preserved. In the exampleof FIG. 22, the array of grating couplers occupy an overall rectangularfootprint. The geometric size of the array does not need to be extendedbeyond the rectangular footprint in order to provide grating couplersfor alignment purposes.

Silicon photonics integrated circuits can have a limit (e.g., softlimit) in the optical power they can handle. Excess optical power mayresult in nonlinear excess waveguide losses. The optical power on thephotonic integrated circuit is kept below certain values to avoid excessnonlinear waveguide losses. A fiber core can carry optical power supplylight that has a power greater than the power that can be properlyhandled by the photonic integrated circuit. An optical power supplylight splitter can split the optical power supply light from a fibercore into two or more optical power supply beams, such that each opticalpower supply beam has a power level appropriate for the photonicintegrated circuit.

Referring to FIG. 23, in some implementations, a fiber-to-PIC connector2300 includes an optical power supply fiber port configured to receiveoptical power supply light 2302 from a polarization-maintaining fiber(PMF) 2304 whose axis is aligned at 45° relative to the walk-off axis ofa walk-off element 2306. The walk-off element 2306 causes half of thelight from the fiber 2304 to go to each of the walk-off paths, resultingin a first optical power supply beam 2308 and a second optical powersupply beam 2310. The first optical power supply beam 2308 is coupled bya first grating coupler 2312 to a photonic integrated circuit 2316, andthe second optical power supply beam 2310 is coupled by a second gratingcoupler 2314 to the photonic integrated circuit 2316. Each gratingcoupler stably receives half of the power carried by thepolarization-maintaining fiber 2304. This way, thepolarization-maintaining fiber 2304 can carry optical power supply lighthaving a power that is twice the amount of power that can be properlyhandled by the photonic integrated circuit 2316.

Referring to FIG. 24A to 24C, in some implementations, an optical powersupply beam from the polarization-maintaining fiber 2304 can be splitinto four beams to allow the polarization-maintaining fiber 2304 tocarry optical power supply light having a power that is four times theamount of power that can be properly handled by the photonic integratedcircuit 2316.

FIG. 24A is a side view of a fiber-to-PIC connector 2400 that includesan optical power supply fiber port configured to receive an opticalpower supply beam 2402 from a polarization-maintaining fiber (PMF) 2304whose axis is aligned at 45° relative to the walk-off axis of a firstwalk-off element 2408. The first walk-off element 2408 causes half ofthe light from the fiber 2304 to go to each of the walk-off paths,resulting in beam 1 (2404) and beam 2 (2406). A quarter-wave plate 2426turns the linearly polarized beam 1 and beam 2 into circularly polarizedbeams. A second walk-off element 2410 performs a second polarizationsplit of the light beams 1 and 2. As a result, beam 1 is split into beam1 a and beam 1 b, whereas beam 2 is split into beam 2 a and beam 2 b.This results in a 1:4 power split. The second walk-off element 2410 isrotated at an angle θ (e.g., 90°) relative to the first walk-off element2408 such that the walk-off direction of the second walk-off element2410 is at the angle θ relative to the walk-off direction of the firstwalk-off element 2408. A subsequent birefringent hole plate rotates thepolarizations of some of the beams to ensure that the polarizationdirections of all of the beams are properly aligned with the gratingcouplers.

FIG. 24B is a second side view of the fiber-to-PIC connector 2400. Thesecond side view is the first side view of FIG. 24A looked at from theright. As shown in FIG. 24B, the second walk-off element 2410 causeshalf of the light from beam 1 (2404) to go to each of the walk-offpaths, resulting in a first beam 1 a and a second beam 1 b. The secondwalk-off element 2410 causes half of the light from beam 2 (2406) to goto each of the walk-off paths, resulting in a third beam 2 a and afourth beam 2 b. A half-wave plate 2412 rotates the second beam 1 b andthe fourth beam 2 b so that the first beam 1 a, the second beam 1 b, thethird beam 2 a, and the fourth beam 2 b have the same polarizationdirection.

FIG. 24C is a diagram showing a position 2414 of the optical powersupply light 2402 that is received from the polarization-maintainingfiber (PMF) 2304. The first walk-off element 2408 causes beam 2 (2406)to be displaced in the first walk-off to a position 2418. Beam 1 remainsat the same position 2414 as the optical power supply light 2402. Thesecond walk-off element 2410 causes beam 1 b to be displaced in thesecond walk-off 2420 to a position 2422. Beam 1 a remains at the sameposition 2414 as beam 1 (2402). The second walk-off element 2410 causesbeam 2 b to be displaced in the second walk-off 2420 to a position 2424.Beam 2 a remains at the same position 2418 as beam 2 (2406).

Beams 1 a, 1 b, 2 a, 2 b are coupled by four grating couplers to aphotonic integrated circuit. Each grating coupler stably receivesone-fourth of the power carried by the polarization-maintaining fiber2304. This way, the polarization-maintaining fiber 2304 can carryoptical power supply light having a power that is four times the amountof power that can be properly handled by the photonic integratedcircuit.

In some examples, instead of using a quarter-wave plate 2426, the secondwalk-off element 2410 can be aligned at 45° relative to the firstwalk-off element 2408 to achieve the same splitting effect.

In some implementations, a third walk-off element is used to split thefour beams 1 a, 1 b, 2 a, 2 b into eight beams. This allows thepolarization-maintaining fiber 2304 to carry optical power supply lighthaving a power that is eight times the amount of power that can beproperly handled by the photonic integrated circuit.

It is possible to use additional walk-off elements to further split thelight beams to allow the polarization-maintaining fiber 2304 to carryoptical power supply light having greater power, such as 16, 32, 64,128, or greater, times the amount of power that can be properly handledby the photonic integrated circuit.

Referring to FIG. 25, coupling an optical power supply to a photonicintegrated circuit can require careful polarization alignment becausemodulators on the photonic integrated circuit can bepolarization-sensitive, i.e., only efficiently modulate one fixed linearpolarization of light. A laser 2500 can emit linearly-polarized light,and a linear-polarization-maintaining fiber (LPMF) 2502 can be used toconnect the external optical power supply 2500 to a photonic integratedcircuit 2504.

Referring to FIG. 26, if one needs more than one power supply input, onecan orient the LPMF 2502 at 45 degrees relative to a polarization beamsplitter (PBS) 2600, thereby achieving a 1:2 optical power split ofoptical supply power at the PBS 2600. In this example, equal power splitmay require accurate angular alignment of the LPMF 2502 at the laser2500 and at the PBS 2600, which can increase the cost of packaging thecomponents.

In some implementations, a circularly-polarized fiber can be used as adistribution fiber for an optical power supply. Referring to FIG. 27, aquarter-wave plate 2700 is provided at the laser 2500 to change thepolarization state of the laser output from linear to circular. Acircular polarization maintaining fiber (CPMF) 2702 transmits thecircular polarized light from the quarter-wave plate 2700 to thepolarization beam splitter 2600. Since circular polarization is asuperposition of two linear polarizations, the PBS 2600 still performs a1:2 power split. An advantage of this design is that the CPMF 2702 canbe mounted to the laser 2500 and to the PBS 2600 at any rotationalangle, reducing the alignment or packaging cost. This generalarchitecture applies to other polarization splitting interfaces as well,including a 2D grating coupler.

For example, the circular polarization maintaining fiber 2702 can bemade of a spun birefringent optical fiber generated by spinning apolarization-maintaining preform during the draw process. The fiber isdesigned to preserve circular polarization: If the input light isright-handed circularly polarized, the output light will also beright-handed circularly polarized; and if the input light is left-handedcircularly polarized, the output light will also be left-handedcircularly polarized. Circular polarization can be viewed as thesuperposition of two linear polarizations with a defined phase angle(e.g., 90°) between them. The circular polarization maintaining fiber2702 preserves the phase angle (e.g., 90°) difference between the twolinear polarizations as these two linear polarizations travel down thefiber.

Referring to FIG. 28, a fiber-to-PIC connector 2800 (same as theconnector 2300 of FIG. 23) receives optical power supply light fromcircular-polarization maintaining fibers 2802. The CPMF fibers 2802 canbe attached relative to the walk-off crystal at any random angle toperform the indicated power split.

The techniques described above for the examples of FIGS. 27 and 28 canalso be used to perform polarization splitting at the input to anedge-coupling interface.

FIG. 29 shows a diagram of a WDM multiplexer 2900. In this example, theWDM multiplexer 2900 can multiplex 4 wavelengths. The same principle canbe used to design a WDM multiplexer that can multiplex N wavelengths, inwhich N is an integer greater than 4. For example, the WDM multiplexer2900 can operate as follows. Four grating couplers 2902 emit 4 signalsat different optical wavelengths (WLs), and all in the samepolarization. A birefringent hole plate 2904 rotates 2 of the 4 WLs,e.g., WL2 and WL4. A graph 2912 shows the polarization directions ofWL1, WL2, WL3, and WL4 after passing the birefringent hole plate 2904. Afirst walk-off element 2906 combines the two polarizations (reverseoperation from the polarization splitting in above embodiments). Awaveplate 2908 shown in red is a higher-order (relatively thick)waveplate whose thickness is designed so as to:

-   -   Not change the polarization of WL1 (“full-wave plate at WL1”);    -   Rotate the polarization of WL2 by 90 degrees (“half-wave plate        at WL2”);    -   Rotate the polarization of WL3 by 90 degrees (“half-wave plate        at WL2”); and    -   Not change the polarization of WL4 (“full-wave plate at WL4”).        A graph 2914 shows the polarization directions of WL1, WL2, WL3,        and WL4 after passing the waveplate 2908. A second walk-off        element 2910 combines the beams (a) at WL1+WL2 of one        polarization and (b) at WL3+WL4 of the orthogonal polarization.        The second walk-off element 2910 has a thickness that is about        twice the thickness of the first walk-off element 2906 because        the displacement between the two beams being combined by the        second walk-off element 2910 is about twice the displacement        between the two beams being combined by the first walk-off        element 2904.

FIG. 30 is a diagram of an example of a WDM multiplexer 3000 thatincludes quartz half-wave plates 3002 and a yttrium orthovanadate (YVO₄)waveplate 3006.

Referring to FIG. 31A, a table 3100 shows 200GBASE-FR4wavelength-division-multiplexed lane assignments. Referring to FIG. 31B,a table 3102 shows 200GBASE-LR4 wavelength-division-multiplexed laneassignments. These lanes provide 800 GHz spacing with 368 GHz window.The center wavelengths of lanes L₀, L₁, L₂, and L₃ in tables 3100 and3102 can correspond to the wavelengths WL1, WL2, WL3, and WL4 in FIGS.29 and 30.

Referring to FIG. 32, a table 3200 shows 400GBASE-FR8wavelength-division-multiplexed lane assignments. The center wavelengthsof the eight lanes in Table 3200 can be used in a WDM multiplexer thathas three walk-off elements that multiplex eight different wavelengths.

The fiber-to-PIC connectors described above can be oriented such thatthe optical axis is parallel or perpendicular (or at any other angle) tothe top surface of the photonic integrated circuit. The optical axis ofthe fiber-to-PIC connector refers to the optical axis of the walk-offelements and the birefringent hole plate.

FIG. 33A is a top view of an example of an optoelectronic device 3300.FIG. 33B is a side view of a first configuration for the optoelectronicdevice 3300, in which a fiber-to-PIC connector has an optical axisparallel to the top surface of a photonic integrated circuit 3304. Alens array 3308 couples light beams that propagate in directionsperpendicular to the top surface of the PIC 3304, and a turning mirror3306 modifies the propagation directions of the light beams.

FIG. 33C is a side view of a second configuration for the optoelectronicdevice 3300, in which a fiber-to-PIC connector 3310 has an optical axisperpendicular to the top surface of the photonic integrated circuit3304. The walk-off elements output light beams that propagate indirections perpendicular to the top surface of the PIC 3304. A turningmirror 3312 modifies the propagation directions of the light beams. Inthe examples of FIGS. 33A to 33C, the turning mirror (e.g., 3306, 3312)changes the directions of the light beams to enable horizontal fiberattachment, i.e., at the attachment locations, the fibers extendparallel to the top surface of the photonic integrated circuit.

FIG. 34A is a side view of a fiber-to-PIC connector 3400 that opticallycouples optical fibers 3402 to a PIC 3404. The fiber-to-PIC connector3400 enables edge coupling of the optical signals.

FIG. 34B is a top view of the fiber-to-PIC connector 3400 that opticallycouples the optical fibers 3402 to the PIC 3404. The fiber-to-PICconnector 3400 enables edge coupling of the optical signals to on-PICwaveguides 3406.

In some implementations, a fiber-to-PIC connector can include afilter-based WDM demultiplexer and/or multiplexer. Such a fiber-to-PICconnector can convert a single row of N fibers to an N×2M array ofgrating couplers, in which M is the number of wavelengths being used.

The fiber-to-PIC connector can include wavelength division multiplexersand/or demultiplexers. FIG. 35 is a side view of an example of afiber-to-PIC connector 3500 that receives wavelength divisionmultiplexed (WDM) optical signals from, or transmits WDM optical signalsto, an optical fiber 3502. In this example, the WDM signals in theoptical fiber 3502 include four wavelengths WL1, WL2, WL3, and WL4.Although the side view of FIG. 35 shows one fiber 3502, it is understoodthat there are more fibers staggered behind the fiber shown.

A first filter 3504 allows optical signals having wavelength WL1 topass, and reflects optical signals having wavelengths WL2, WL3, and WL4.A second filter 3506 reflects optical signals having wavelength WL2, andallows optical signals having wavelengths WL3 and WL4 to pass. A thirdfilter 3508 reflects optical signals having wavelength WL3 and allowsoptical signals having wavelength WL4 to pass. A wavelength-independentmirror 3510 reflects optical signals having wavelength WL4.

When the fiber-to-PIC connector 3500 is used as a demultiplexer, a WDMoptical signal having components having wavelengths WL1, WL2, WL3, andWL4 (two polarizations for each wavelength) is separated by the filters3504, 3506, and 3508 into four optical signals, each having onewavelength. The four single-wavelength optical signals pass a walk-offelement 3512 and a birefringent hole plate 3514, resulting in eightoptical signals having the same polarization state that are properlyaligned to the grating couplers 3516. When the fiber-to-PIC connector3500 is used as a multiplexer, the optical signals having wavelengthsWL1, WL2, WL3, and WL4 from the grating couplers 3516 pass thebirefringent hole plate 3514 and the walk-off element 3512, and aredirected by the filters 3504, 3506, 3508, and mirror 3510 to the fiber3502.

FIG. 36 shows diagrams of examples of an arrangement of fiber ports3600, a birefringent hole plate 3602, and an array of grating couplers3604. For demultiplexing, a WDM optical signal from each fiber port 3600is split into eight optical signals having four different wavelengths.For multiplexing, eight optical signals having four differentwavelengths from the grating couplers 3604 are multiplexed into a WDMoptical signal and directed to the fiber port 3600.

FIG. 37 is a diagram showing an example of waveguide routing from thegrating couplers to on-PIC modulators. Two rows of grating couplers 3702process optical signals having the wavelength WL1. The next two rows ofgrating couplers 3704 process optical signals having the wavelength WL2.The next two rows of grating couplers 3706 process optical signalshaving the wavelength WL3. The next two rows of grating couplers 3708process optical signals having the wavelength WL4.

A first set of modulators 3710 process optical signals havingwavelengths WL1 and WL2. A second set of modulators 3712 process opticalsignals having wavelengths WL3 and WL4. Each modulator has an input port3714 that receives optical power supply light, and an output port 3716for outputting transmit signals. In this example, the grating couplersthat process wavelengths WL1 and WL2 are on a first side of the array ofgrating couplers near the first set of modulators 3710. The gratingcouplers that process wavelengths WL3 and WL4 are on a second side ofthe array of grating couplers near the second set of modulators 3712.This avoids crossing of the waveguides and makes it easier to design thewaveguide routing.

Referring to FIG. 38, in some implementations, a fiber-to-PIC connector3800 is configured to couple to multiple rows of optical fibers 3802.The figure shows a side view of the fiber-to-PIC connector 3800, inwhich two fibers 3802 from two rows are shown. It is understood thatthere are more fibers staggered behind the fibers shown. The connector3800 can convert K rows of N fibers (e.g., fiber (a), fiber (b)) to anN×2MK array of grating couplers, in which M represents the number ofwavelengths being used. In this example, M=4 wavelengths are used.

The fiber-to-PIC connector 3800 includes a first filter 3804 that allowsoptical signals having wavelength WL1 to pass, and reflects opticalsignals having wavelengths WL2, WL3, and WL4. A second filter 3806reflects optical signals have wavelength WL2, and allows optical signalshaving wavelengths WL3 and WL4 to pass. A third filter 3808 reflectsoptical signals have wavelength WL3 and allows optical signals havingwavelength WL4 to pass. A wavelength-independent mirror 3810 reflectsoptical signals have wavelength WL4. The filters 3804, 3806, and 3808are sufficiently large to enable processing of the light beams from thetwo fibers 3802. In this example, the two input beams are split into 16beams that are directed to the grating couplers.

FIG. 39 is a diagram of an example of a fiber-to-PIC connector 3900 thatincludes a filter-based wavelength division demultiplexer andmultiplexer, which includes broadband optical splitters of varyingsplitting ratio and bandpass optical filters. The fiber-to-PIC connector3900 includes a first broadband optical splitter that has a 25%:75%splitting ratio, such that 25% of the light passes the splitter to forma beam 3904, and 75% of the light is reflected to form a beam 3906. Thebeam 3904 passes a walk-off element 3908 that splits the beam 3904 intotwo polarized beam 3912 a and 3912 b. The polarized beams 3912 a, 3912 bare filtered by a first bandpass optical filter 3910 that allowswavelength WL1 to pass through.

The beam 3906 is directed towards a second broadband optical splitter3918 that has a 33%:67% splitting ratio, such that 33% of the beam 3906is reflected by the splitter 3918 to form a beam 3914, and 67% of thebeam 3906 passes through the splitter 3918 to form a beam 3916. The beam3914 has about 75%×33%=25% of the power of the input beam 3922 from thefiber 3924. The beam 3916 has about 75%×67%=50% of the power of theinput beam 3922. The beam 3914 passes the walk-off element 3908, whichsplits the beam 3914 into two polarized beams that are filtered by asecond bandpass optical filter 3920 that allows wavelength WL2 to passthrough.

The beam 3916 is directed towards a third broadband optical splitter3922 that has a 50%:50% splitting ratio, such that 50% of the beam 3916is reflected by the splitter 3922 to form a beam 3924, and 50% of thebeam 3916 passes through the splitter 3922 to form a beam 3926. Each ofthe beams 3924 and 3926 has about 50%×50%=25% of the power of the inputbeam 3922. The beam 3924 passes the walk-off element 3908, which splitsthe beam 3924 into two polarized beams that are filtered by a thirdbandpass optical filter 3928 that allows wavelength WL3 to pass through.

The beam 3926 is directed towards a turning mirror 3930 that reflects100% of the beam 3926 towards the walk-off element 3908, which splitsthe beam 3926 into two polarized beams that are filtered by a fourthbandpass optical filter 3932 that allows wavelength WL4 to pass through.

In some implementations, the bandpass optical filters 3910, 3920, 3928,and 3932 can be used in the multiplexer and demultiplexer of FIGS. 35and 38 to lower inter-channel crosstalk.

In some implementations, non-reciprocal optical elements can be used toform an isolator. Referring to FIG. 40, a fiber-to-PIC connector 4000includes an isolator such that light leaving the photonic integratedcircuit (egress, blue arrows) does not retrace the input (ingress)optical path (red arrows) and consequently does not couple back intooptical fibers. The principle also applies to the greyed-out orthogonalpolarization.

An incoming beam 4004 is split by a walk-off element 4002 into a firstingress beam 4008 having a polarization A and a second ingress beam 4010having a polarization A′. A −45° rotation half-wave plate 4006 rotatesthe polarization of the first ingress beam 4008 to have a polarizationB. The first ingress beam 4008 then passes a +45° Faraday rotator 4012to have a polarization C, which is aligned with a grating coupler 4016.The polarization directions A, B, and C are shown in a diagram 4014 atthe upper part of the figure.

An egress beam initially has a polarization C. The egress beam passesthe +450 Faraday rotator 4012 to have a polarization B. The walk-offelement 4002 changes the propagation direction of the egress beam tobecome beam 4018 that does not retrace the input (ingress) optical pathand consequently does not couple back into the optical fiber 4020.

Referring to FIG. 41, which is similar to FIG. 10B, the incoming beam1008 from the fiber core 302 passes the collimating lens 551 and issplit by the walk-off crystal 1004 into two beams 755 a and 755 b (seeFIG. 10A), which pass the birefringent hole plate 1006, the second lens541, and the third lens 542, and are directed to the vertical couplingelements 231 on the photonic integrated circuit 210 at an angle ofincidence θ. In some implementations, the angle of incidence θ can be ina range, e.g., from 10 to 30°, 10 to 16°, or 4° to 12°, or about 8°,depending on the design of the vertical coupling elements 231, which canbe, e.g., vertical grating couplers.

In some implementations, each third lens 542 is a rotationally symmetricspherical lens. In order to direct the light beams (e.g., 755 a and 755b) toward the grating couplers at the desired angle of incidence θ, thefiber core 302, the collimating lens 551, the walk-off crystal 1004, thebirefringent hole plate 1006, and the second lens 541 are positionedrelative to the third lens 542 such that each light beam propagatesalong a beam path that is parallel to the optical axis of the third lens542, and the center axis of the beam path is spaced apart at an offsetdistance from the optical axis of the third lens 542. The gratingcoupler 231 is positioned near the focal plane of the third lens 542,and the optical axis of the third lens 542 passes the location on thegrating coupler 231 where the light beam is intended to be focused,i.e., the focal point. The light beam is refracted by the third lens 542toward the focal point with an angle of incidence θ. The offset distanceand the focal distance of the third lens 542 are selected to achieve thedesired angle of incidence θ. For example, increasing the offsetdistance and/or reducing the focal distance of the third lens 542results in a greater angle of incidence θ.

In the example above, in order to achieve the desired offset between thecenter axis of the light beam and the optical axis of the third lens542, the diameter of the light beam is made smaller than the diameter ofthe third lens 542. In an optical system in which the propagating beamis centered on the optical axis, rotationally symmetric spherical lensshapes provide adequate area usage when arranged in an array. However,in case of an off-axis beam as described above and shown in FIG. 41,only a fraction of the lens area is used, depending on the offset of thebeam from the optical axis. In case of large beam offsets, only a smallfraction of the lens area is used, which limits the density ofindividual beams being propagated through a system of lens arrays.

One aspect of robust optical system design relates to the diameter ofthe optical beams traversing the system. Too small beam diameters resultin too quickly diverging optical beams, which limits the longitudinaldistance over which collimated beams can be propagated. For example, abeam of diameter of 100 μm at a wavelength of 1.5 μm results in a beamof diameter about 138 μm over a propagation distance of 5 mm. It istherefore important to make collimated beams wide enough in order topropagate them through optical systems (e.g., the fiber-to-PIC connector1000 of FIGS. 10A, 10B, 12, 13A) without excessive broadening. In densearrays, such as the examples shown in FIGS. 20A to 20C, beam diametersare upper-bounded by the distance between adjacent beams within thearray.

In some implementations, to improve the area usage, increase the densityof individual beams propagated through the system of lens arrays, andincrease the beam diameters to the extent possible, an array ofcircularly asymmetric or rotationally asymmetric optical lenses areprovided in which each rotationally asymmetric optical lens has asurface profile similar to a conventional rotationally symmetric opticallens that is truncated such that only the part of the rotationallysymmetric optical lens that is intersected by the offset light beam isimplemented. This allows the unused area of the conventional lens to beavailable for use by other rotationally asymmetric optical lenses in thearray, thereby increasing the density of individual beams, as comparedto using an array of conventional rotationally symmetric optical lenses.

The following describes examples of an array of circularly asymmetric orrotationally asymmetric optical lenses configured to couple an array ofincoming beams to an array of vertical coupling elements, e.g., gratingcouplers, on an active layer of a photonic integrated circuit at anangle of incidence, e.g., in a range from 10 to 30°, 10 to 16°, or 4° to12°, or about 8°, depending on the design of the vertical couplingelements. For example, if the grating couplers are designed to emitlight at an angle θ relative to the normal direction of the main surfaceof the photonic integrated circuit, then the circularly asymmetricoptical lenses are designed such that the incoming beams are focusedonto the grating couplers with an angle of incidence equal to 6. Thegrating couplers are design to reduce the amount of reflection at theinterface between the grating couplers and the optical waveguidescoupled to the grating couplers.

For example, the circularly asymmetric optical lenses can be free-formoptical lenses, which can be free-form off-axis optical lenses. Thecircularly asymmetric optical lenses can be made by, e.g., grayscalelithography and subsequent etching or 3D printing. The circularlyasymmetric optical lenses can be made of, e.g., silicon, glass, or apolymer-based material.

FIG. 42 shows a top view and a side view of an example of a circularlyasymmetric (or rotationally asymmetric) optical lens 4200 that focusesan offset light beam 4202 onto a vertical coupling element 4204 at anangle of incidence θ. The vertical coupling element 4204 can be, e.g., avertical grating coupler, which can be positioned near the focal plane4214 of the circularly asymmetric optical lens 4200. The verticalcoupling element 4204 is coupled to an optical waveguide 4210 thatcarries the light received at the vertical coupling element 4204 toother parts of the photonic integrated circuit. An array of thecircularly asymmetric optical lens 4200 can be used in, e.g., thefiber-to-PIC connector 1000.

The circularly asymmetric optical lens 4202 is circularly asymmetric, orrotationally asymmetric, with respect to an optical axis 4206. Thecircularly asymmetric optical lens 4202 can be regarded as implementingonly a portion of a circularly symmetric optical lens 4208, shown indashed lines, that is intersected by the offset light beam 4202. Thecircularly symmetric optical lens 4208 is rotationally symmetric withrespect to the optical axis 4206. In the example shown in FIG. 42, thedimension of the circularly asymmetric optical lens 4200 (measured alonga direction parallel to the main surface of the photonic integratedcircuit and on a plane that aligns with the optical axis 4206) isslightly larger than the radius of the circularly symmetric lens 4208.In some implementations, depending on the offset between the light beam4202 and the optical axis 4206, the dimension of the circularlyasymmetric optical lens 4200 can be, e.g., 80%, 70%, 60%, 50%, 40%, 30%,or 20%, or any value in the range from 20% to 80% of the diameter of thecircularly symmetric lens 4208. By using a smaller circularly asymmetricoptical lens 4200 that occupies a smaller area as compared to thecircularly symmetric lens 4208, the freed-up space can be used by othercircularly asymmetric optical lenses, enabling a higher density of lightbeams 4202 to be coupled to a correspondingly higher density of gratingcouplers 4204.

The description above relates to how the circularly asymmetric lens 4200focuses the light beam 4202 onto the grating coupler 4204 at an angle ofincidence θ. The same principle operates in the reverse, i.e., thegrating coupler 4204 can emit light toward the circularly asymmetriclens 4200 at an exit angle θ, and the circularly asymmetric lens 4200collimates the light to form a collimated light beam that is coupled tothe corresponding optical fiber core (e.g., 302).

In the example of FIG. 42, the circularly asymmetric optical lens 4200has a circular outer circumference as viewed in the direction of thebeam path, as if a circular cutout was made from the circularlysymmetric lens 4208. A circularly asymmetric optical lens does notnecessarily have a circular outer circumference or footprint. The outercircumference or footprint of the circularly asymmetric optical lens canbe, e.g., a circle, an oval, a square, a rectangle, a polygon, or anyarbitrary shape. The circumference of each circularly asymmetric opticallens 4200 is designed such that the circularly asymmetric lens 4200 canreceive as much of the light beam 4202 as possible to achieve a desiredsignal-to-noise ratio, while adjacent circularly asymmetric opticallenses 4200 are packed as dense as possible without causing interferenceor crosstalk between adjacent beams.

In some implementations, the circumference or footprint of thecircularly asymmetric optical lens 4200 corresponds to thecross-sectional shape of the offset light beam 4202. For example, if theoffset light beam 4202 has a circular or oval cross-section, thecircularly asymmetric optical lens 4202 is also designed to have acorresponding circular or oval circumference or footprint.

The circularly asymmetric lens 4200 includes an upper surface having aprofile or curvature that matches the surface profile or curvature ofthe circularly symmetric lens 4208. The surface profile or curvature ofthe circularly asymmetric lens 4200 can correspond to the curvature of aspherical lens. The surface profile or curvature of the circularlyasymmetric lens 4200 can correspond to the curvature of an asphericallens, e.g., in order to correct one or more optical aberrations. Forexample, in a wavelength divisional multiplexed system, the light beam4202 carries multiple wavelengths, and the circularly asymmetric opticallenses having aspherical surface profiles can be designed to correctchromatic aberrations to maximize the coupling efficiency at the gratingcouplers. Such circularly asymmetric optical lenses can be made usingtechniques that are used to produce free-form lenses.

The circularly asymmetric lens 4200 has an edge 4212 along the outercircumference, which is outside of the area intersected by the lightbeam 4200. The edge 4212 can be parallel to the optical axis 4206,sloped at an angle relative to the optical axis 4206, have a step shape,or an arbitrary shape.

In some implementations, the light beam 4202 is a Gaussian beam, and thearea of the light beam 4200 refers to the region having an intensitythat is at least half of the peak intensity of the light beam 4202. Theedge of the light beam 4202 having an intensity that is less than halfof the peak intensity can extend to or beyond the circumference of thecircularly asymmetric lens 4200, so the reflection and/or refraction atthe edge 4212 are taken into account in the design of the overall arrayof circularly asymmetric lenses 4200. The geometry of each individualcircularly asymmetric lens 4200 and the spacing between adjacentcircularly asymmetric lenses 4200 are selected so that the interferenceand/or cross-talk between the light beams are negligible.

FIG. 43 is a diagram showing a top view and a side view of an array ofcircularly asymmetric optical lenses 4200 that focus the light beams4202 toward the vertical grating couplers 4204 at an angle of incidenceθ that matches the design of the grating couplers 4204 so as to increasethe coupling efficiency at the grating couplers 4204 and reduce thereflections at the interfaces between the grating couplers 4204 and theoptical waveguides 4210.

The circularly asymmetric lens 4200 a occupies a fraction of the area ofa conventional circularly symmetric lens 4208 shown in dashed lines. Thecircularly asymmetric lens 4200 implements a portion of the rotationallysymmetric optical lens 4208 that is intersected by the offset light beam4202. The freed-up unused area is used by other circularly asymmetriclenses 4200. In this example, the adjacent circularly asymmetric lenses4200 b, 4200 c, 4200 d overlap the area of the circularly symmetric lens4208, so packing the light beams 4202 as densely as shown in FIG. 43would be difficult if an array of circularly symmetric lens 4208 wereused.

In this example, the distance between adjacent optical fiber cores 302is about 250 μm, and the distance between two nearest adjacentcircularly asymmetric lenses 4200 is about 125√{square root over (2)}μm. The edge 4212 near the optical axis 4206 has a step height of about14 μm. The walk-off direction of the walk-off crystal 1004 is in thediagonal direction represented by the arrow 4300. For example, anoptical beam from an optical fiber core 302 aligned with a circularlyasymmetric lens 4200 e is split off by the wall-off crystal 1004 intotwo beams that are aligned with the circularly asymmetric lens 4200 eand a circularly asymmetric lens 4200 f, which focus the two beamstoward two corresponding grating couplers at the specified angle ofincidence.

FIG. 44 is a diagram showing a top view and a side view of an array ofcircularly symmetric optical lenses 4208 that focus the light beams 4202toward the vertical grating couplers 4204 at an angle of incidence θthat matches the design of the grating couplers 4204 so as to increasethe coupling efficiency at the grating couplers 4204 and reduce thereflections at the interfaces between the grating couplers 4204 and theoptical waveguides 4210. The diameter of the light beam 4202 is lessthan half of the diameter of the circularly symmetric optical lens 4208.If a fiber-to-PIC connector uses the array of circularly symmetricoptical lenses 4208, the distance between the optical fiber cores 302will be about 450 μm, and the distance between two nearest adjacentcircularly symmetric lenses 4208 will be about 225√{square root over(2)} μm. A comparison of FIGS. 43 and 44 shows the advantage of thearray of circularly asymmetric lens 4200 in that the array of circularlyasymmetric lens 4200 allow the light beams 4202 to be more denselypacked without reducing the cross-section size of the light beams,allowing the optical fiber cores 302 to be more densely packed so thatmore optical fiber cores can be packed inside an optical fiber cable ofa given size, and enabling higher data throughput for an opticalcommunication system that has a finite area (e.g., area in the frontand/or rear panel) allocated for connecting to optical fiber cables.

Off-axis optical beams commonly occur when coupling light from and to aphotonic integrated circuit (PIC) using grating couplers. These devicesimplemented on the PIC can in principle be designed for arbitraryemission angles. However, usually off-axis designs are preferred (forexample emission at 8 degrees), because this allows to reduce thereflection of the component. For many applications of PICs a lowreflection or high return loss of the grating coupler is desirable inorder to achieve the intended functions.

FIG. 45A is a diagram showing an example of a fiber-to-PIC connector4500 that uses an array of circularly asymmetric optical lenses 4200.The fiber-to-PIC connector 4500 is used for coupling optical fibers to aphotonic integrated circuit that has grating couplers 4502 that emitlight beams at an exit angle θ, e.g., in a range from 1° to 30°, orabout 8°. When lightwave signals are transmitted from optical waveguidesto the grating couplers 4502, the reflection can be smaller (as comparedto the example shown in FIG. 45B).

In this example, similar to the example of FIG. 43, the distance betweenadjacent optical fiber cores 302 is about 250 μm, and the distancebetween two nearest adjacent circularly asymmetric lenses 4200 is about125√{square root over (2)} μm. Each circularly asymmetric lens 4200 hasa circular circumference (as viewed in the direction of the beam path)that has a diameter of about 160 μm, and the offset distance between thegeometric center of the circularly asymmetric lens 4200 (as viewed alongthe direction of the beam path) and the optical axis is about 45√{squareroot over (2)} μm. The radius of the surface curvature of the circularlyasymmetric lens 4200 is about 610 μm. The distance between thecircularly asymmetric lens 4200 and the focal plane 4214 is about 1 mm.The parameter values listed above are merely examples, other values canalso be used.

FIG. 45B is a diagram showing an example of a fiber-to-PIC connector4504 that uses an array of circularly symmetric optical lenses 4506. Thefiber-to-PIC connector 4504 is used for coupling optical fibers to aphotonic integrated circuit that has grating couplers 4508 that emitlight beams vertically, i.e., at an exit angle θ=0. When lightwavesignals are transmitted from optical waveguides to the grating couplers4508, the reflection can be larger (as compared to the example shown inFIG. 45A).

In this example, the distance between adjacent optical fiber cores 302is about 250 μm, and the distance between two nearest adjacentcircularly symmetric lenses 4506 is about 125√{square root over (2)} μm.Each circularly symmetric lens 4506 has a diameter of about 160 μm. Theradius of the surface curvature of the circularly symmetric lens 4506 isabout 610 μm. The distance between the circularly asymmetric lens 4506and the focal plane 4214 is about 1 mm. The parameter values listedabove are merely examples, other values can also be used.

In some implementations, the end facets of fiber arrays (FAs) arepolished at an angle, e.g., in a range of 4° to 12°, or about 8 degrees,to achieve a high return loss. Therefore, when interfacing a PIC with afiber array via a micro-optic assembly that includes lens arrays andother optical components, on-axis designs are less preferred. On theother hand, implementing an off-axis design with the same diameter ofthe collimated beam using an array of conventional lenses, restricts thedensity of the array. Hence, the array of circularly asymmetric lenses(e.g., 4200) is a solution that enables a dense array of collimatedbeams for a high return loss interface from the photonic integratedcircuit to the fiber array.

FIGS. 46A and 46B show diagrams that illustrate how the array ofcircularly asymmetric lenses (e.g., 4200), which can be free-formlenses, enables a larger beam diameter d2>d1 compared to a design withconventional array of circularly symmetric lenses (e.g., 4208) that hasthe same density of beams.

FIGS. 46A and 46B illustrate how an array of circularly asymmetriclenses enable larger beam diameters as compared to a design using anarray of conventional circularly symmetric lenses that has the samedensity of light beams.

FIG. 46A is a diagram showing an example of a fiber-to-PIC connector4600 that couples an array of grating couplers 4602 to a fiber array4604 with end facets polished at an angle of about 8 degrees. Thefiber-to-PIC connector 4600 includes a first array of circularlyasymmetric lenses 4608 and a second array of circularly asymmetriclenses 4610. For example, the first array of circularly asymmetriclenses 4608 can have the same surface curvature as that of the secondarray of circularly asymmetric lenses 4610, except that the concavesurfaces of the lenses 4608 face the concave surfaces of the lenses4610. The first array of circularly asymmetric lenses 4608 receive light4612 emitted from the grating couplers 4602 at an exit angle of 8°, andcollimate the light 4612 to produce collimated light beams 4614. Thesecond array of circularly asymmetric lenses 4610 focus the collimatedlight beams 4614 toward the optical fiber cores of the fiber array 4604,in which the paths of the focused light beams 4616 are at an angle of 8°relative to the paths of the collimated light beams 4614. This way, thefocused light beams 4616 are aligned with the optical fiber cores of thefiber array 4604. The diameter of the collimated light beams 4614 is d2.

FIG. 46B is a diagram showing an example of a fiber-to-PIC connector4620 that couples an array of grating couplers 4602 to a fiber array4604 with end facets polished at an angle of about 8 degrees. Thefiber-to-PIC connector 4620 includes a first array of circularlysymmetric lenses 4622 and a second array of circularly symmetric lenses4624. The first array of circularly symmetric lenses 4622 can have thesame surface curvature as that of the second array of circularlysymmetric lenses 4624, except that the concave surfaces of the lenses4622 face the concave surfaces of the lenses 4624. The first array ofcircularly symmetric lenses 4622 receive light 4626 emitted from thegrating couplers 4602 at an exit angle of 8°, and collimate the light4612 to produce collimated light beams 4628. Each light beam 4626 onlyintersects a fraction of the corresponding circularly symmetric lens4622. The second array of circularly symmetric lenses 4624 focus thecollimated light beams 4628 toward the optical fiber cores of the fiberarray 4604, in which the paths of the focused light beams 4630 are at anangle of 8° relative to the paths of the collimated light beams 4628.This way, the focused light beams 4628 are aligned with the opticalfiber cores of the fiber array 4604. The diameter of the collimatedlight beams 4628 is d1. Because only fractions of the circularlysymmetric lenses 4622 and 4624 are used to process (e.g., refract) thelight beams 4626 and 4628, the light beams 4628 have smaller diametersas compared to the light beams 4614, i.e., d1<d2. The increased beamdiameter d2 significantly relaxes the assembly tolerances of themicro-optic system resulting in an improved manufacturability.

Referring to FIG. 47, in some implementations, an array of circularlyasymmetric lenses can be combined with a conventional lens array (anarray of circularly symmetric lenses) when interfacing an array ofgrating couplers on a PIC that emit at an angle of 8 degrees with afiber array polished at an angle of 0 degree. For example, afiber-to-PIC connector 4700 is configured to couple an array of gratingcouplers 4602 to a fiber array 4702 with 0 degree polish. Thefiber-to-PIC connector 4700 includes a first array of circularlyasymmetric lenses 4608 that collimate the light from the gratingcouplers 4602, and a second array of circularly symmetric lenses 4624that focus the collimated light beams toward the optical fiber cores ofthe fiber array 4702.

Referring to FIG. 48, in some implementations, an assembly of twodifferent (mirror-symmetric) versions of the array of circularlyasymmetric lenses are combined to interface an array of grating couplerson a PIC that emit at an angle of 8 degrees with a fiber array polishedat an angle of −8 degrees. For example, a fiber-to-PIC connector 4800 isconfigured to couple an array of grating couplers 4602 to a fiber array4802 with −8 degree polish. The fiber-to-PIC connector 4800 includes afirst array of circularly asymmetric lenses 4608 that collimate thelight from the grating couplers 4602, and a second array of circularlyasymmetric lenses 4804 that focus the collimated light beams toward theoptical fiber cores of the fiber array 4802. In this example, the secondarray of circularly asymmetric lenses 4804 is mirror-symmetric relativeto the first array of circularly asymmetric lenses 4608.

Referring to FIG. 49, in some implementations, two identical arrays ofcircularly asymmetric lenses are used for a smart connector assembly aspreviously described. In this example, a fiber-to-PIC connector 4900includes a second array of circularly asymmetric lenses 4610 thatcollimates the light emitted from the fiber array 4604 with 8° polish.The fiber-to-PIC connector 4900 includes a walk-off crystal 4902 thatsplits the incoming collimated beam 4904 into two beam components 4906 aand 4906 b, which pass through a birefringent hole plate 4908 (which canbe a half-wave plate with openings) in which one beam component has itspolarization rotated 90° so that the two beam components 4906 a and 4906b have the same polarization direction. The beam components 4906 a and4906 b are focused by the array of circularly asymmetric lenses 4608toward the array of grating couplers 4602 at the appropriate angle ofincidence.

In this example, only for the first lens array 4608 nearer to thegrating coupler array 4602 the full density of the collimated beams isrequired. Only every second lens is used in the second array of lenses4610 facing the fiber array 4604. Thus, the second lens array can alsobe implemented as an array of conventional circularly symmetric lenses.In some implementations, the fiber array is implemented with a 0 degreepolish, then the second array of lenses facing the fiber array isimplemented as an array of conventional circularly symmetric lenses asshown in the example of FIG. 47.

The following describes examples of using circular polarizationmaintaining fibers (CPMF) to transmit light from lasers to modulators.

Referring to FIG. 54, in some implementations, an optoelectronic dataprocessing system 5400 includes a laser 5402, a first quarter-wave plate5404, a circular polarization maintaining fiber (CPMF) 5406, a secondquarter-wave plate 5408, a modulator 5410, and other data processingmodules not shown in the figure. The laser 5402 provides optical powersupply light to the modulator 5410. The laser 5402 generates linearlypolarized light, and the first quarter-wave plate 5404 converts thelinearly polarized light to circularly polarized light.

While the examples described in FIGS. 54 to 60 use one or more circularpolarization maintaining fibers as a mechanism to couple a “laser” to a“modulator,” the described technique can be used to generally couple anyfirst device emitting a linear state of polarization to any seconddevice intended to receive a linear state of polarization. The firstlinearly polarized device does not have to be a laser but can be anydevice emitting linearly polarized light. The second linearly polarizeddevice does not have to be a modulator but can be any device thatpreferably accepts linearly polarized light. Examples of the secondlinearly polarized device include: (a) A lithium niobate opticalmodulator; (b) a vertical grating coupler on a photonic integratedcircuit; (c) a modulator integrated on a photonic integrated circuit.For example, the first linearly polarized device can be a localoscillator that generates a sequence of optical pulses, and the secondlinearly polarized device can be a coherent optical receiver. Forexample, the first linearly polarized device can be asingle-polarization optical transmitter, and the second linearlypolarized device can be a single-polarization optical receiver.

The circular polarization maintaining fiber (CPMF) 5406 transmits thecircularly polarized light from the first quarter-wave plate 5404 to thesecond quarter-wave plate 5408 while maintaining the polarization stateof the circularly polarized light. The region between the firstquarter-wave plate 5404 and the second quarter-wave plate 5408 forms arotationally invariant region. The term “rotationally invariant region”in this context refers to a region that includes one or more segments ofcircular polarization maintaining fiber that are connected to each otheras well as to the first and second quarter-wave plates through opticalconnections. Due to the circular polarization maintaining nature of thecircular polarization maintaining fiber, these connections do not haveto be rotationally aligned. The second quarter-wave plate 5408 convertsthe circularly polarized light to linearly polarized light that ispassed to the modulator 5410. The modulator 5410 can be, e.g., part of aphotonic integrated circuit 2504 (FIG. 27) or part of any otheroptoelectronic module.

An advantage of this design is that the circular polarizationmaintaining fiber 5406 can be mounted to the first quarter-wave plate5404 and the second quarter wave plate 5408 at any rotational angle,reducing the alignment or packaging cost. The two ends of the circularpolarization maintaining fiber 5406 can be randomly rotated without aneffect on the linear polarization orientation generated after the secondquarter-wave plate 5408, as long as the linear polarization of the laser5402 is oriented correctly with respect to the first quarter-wave plate5404, and the second quarter-wave plate 5408 is oriented correctly withrespect to the modulator 5410. The critical rotational alignment is notat the ends of the optical fiber, but rather at the quarter-wave plates5404 and 5408. Because the quarter-wave plates 5404 and 5408 areattached to the laser 5402 and the modulator 5410, respectively, duringdevice assembly, this is overall likely to be more convenient and/orcheaper than making sure that the optical fiber is rotationally alignedat each fiber connector along the way.

Referring to FIG. 55, in some implementations, an optoelectronic dataprocessing system 5500 includes a laser array 5502, a first singlequarter-wave plate 5504, a plurality of circular polarizationmaintaining fibers (CPMFs) 5506, a second single quarter-wave plate5508, a modulator array 5510, and other data processing modules notshown in the figure. The laser array 5502 includes a plurality of lasersthat have aligned polarizations, and can have the same wavelength ordifferent wavelengths. The laser array 5502 provides optical powersupply light to the modulator array 5510. The modulator array 5510includes a plurality of modulators, which can be disposed on, e.g., aphotonic integrated circuit. The circular polarization maintainingfibers (CPMFs) 5506 transmit light from the laser array 5502 to themodulator array 5510, in which the light from each laser is transmittedthrough one of the polarization maintaining fibers 5506 to acorresponding modulator.

The first single quarter-wave plate 5504 covers all laser outputs andconverts the linearly polarized laser outputs to respective circularlypolarized light. Each of the circular polarization maintaining fibers(CPMFs) 5506 transmits circularly polarized light from the first singlequarter-wave plate 5504 to the second single quarter-wave plate 5508.The second single quarter-wave plate 5508 converts the circularlypolarized light from all of the circular polarization maintaining fibers5506 to linearly polarized light that are passed to respectivemodulators. The second single quarter-wave plate 5508 can beedge-coupled or vertically coupled to the photonic integrated circuitthat includes the array of modulators. The region between the firstsingle quarter-wave plate 5504 and the second single quarter-wave plate5508 forms a rotationally invariant region.

Each of the lasers in the laser array 5502 generates linearly polarizedlight. A first laser generates a first linearly polarized light, and asecond laser generates a second linearly polarized light. When we saythat the first laser and the second laser have aligned polarizations, wemean that the first linearly polarized light has a polarizationdirection that is substantially parallel to the polarization directionof the second linearly polarized light. The term “substantiallyparallel” is meant to take into account tolerances in the manufacturingand/or assembling process. For example, in some contexts, two directionscan be “aligned” or “substantially parallel” when the angle between thetwo directions is within 10°, or within 5°, or within 1°. Similarly, insome contexts, two directions can be “substantially orthogonal” when theangle between the two directions is within a range of 800 to 100°, orwithin a range of 85° to 95°, or within a range of 89° to 91°.

An advantage of this design is that each of the circular polarizationmaintaining fibers 5506 can be mounted to the first single quarter-waveplate 5504 and the second single quarter wave plate 5508 at anyrotational angle, reducing the alignment or packaging cost.

Referring to FIG. 56, in some implementations, an optoelectronic dataprocessing system 5600 includes a first photonic integrated circuit 5602and a second photonic integrated circuit 5604. The first photonicintegrated circuit 5602 includes an array of lasers 5606 and a firstarray of individual quarter-wave polarization rotators 5608. The secondphotonic integrated circuit 5604 includes a second array of individualquarter-wave polarization rotators 5610 and an array of modulators 5612.The array of lasers 5606 provide optical power supply light to the arrayof modulators 5612.

A plurality of circular polarization maintaining fibers (CPMFs) 5614 areoptically coupled to the first array of individual quarter-wavepolarization rotators 5608 and the second array of individualquarter-wave polarization rotators 5610. The region between the firstarray of individual quarter-wave polarization rotators 5608 and thesecond array of individual quarter-wave polarization rotators 5610 formsa rotationally invariant region. The circular polarization maintainingfibers 5614 can be edge-coupled or vertically coupled to the photonicintegrated circuit 5604. The laser 5606 generates linearly polarizedlight that is converted to circularly polarized light by the firstindividual quarter-wave polarization rotator 5608. The circularlypolarized light is transmitted by the circular polarization maintainingfiber 5614 to the second individual quarter-wave polarization rotator5610, which converts the circularly polarized light to linearlypolarized light that is passed on to the modulator 5612.

In the example above, the array of lasers 5606 and the array ofindividual quarter-wave polarization rotators 5608 can be integrated ona substrate or a module that is different from a photonic integratedcircuit. Similarly, the array of individual quarter-wave polarizationrotators 5610 and the array of modulators 5612 can be integrated on asubstrate or a module that is different from a photonic integratedcircuit.

An advantage of this design is that the circular polarizationmaintaining fibers 5614 can be mounted to the first individualquarter-wave polarization rotators 5608 and the second photonicintegrated circuit 5604 at any rotational angle, reducing the alignmentor packaging cost.

The following describes examples in which a single circular polarizationmaintaining fiber is used to transmit photon supply light to twomodulators.

Referring to FIG. 57, in some implementations, an optoelectronic dataprocessing system 5700 includes an optical power supply source 5702 anda photonic integrated circuit 5704, in which a circular polarizationmaintaining fiber 5706 is optically coupled between the optical powersupply source 5702 and the photonic integrated circuit 5704. The regionbetween the optical power supply source 5702 and the photonic integratedcircuit 5704 forms a rotationally invariant region.

The optical power supply source 5702 includes a first laser 5708 a and asecond laser 5708 b. The first laser 5708 a generates a first laserlight having a first linear polarization, and the second laser 5708 bgenerates a second laser light having a second linear polarization. Forexample, the first linear polarization can be substantially orthogonalto the second linear polarization. The first and second laser lights arecombined at a polarization beam splitter 5710 to generate a firstcombined light 5712 having a first component and a second component, inwhich the first component has the first linear polarization and thesecond component has the second linear polarization. A firstquarter-wave plate 5714 converts the first combined light 5712 to secondcombined light 5716, which in this example is a circularly polarizedcombined light. The second combined light 5716 includes a firstcomponent having a first circular polarization (e.g., right-handedcircular polarization) and a second component having a second circularpolarization (e.g., left-handed circular polarization). The firstcomponent (having the first linear polarization) of the first combinedlight 5712 is converted by the quarter-wave plate 5714 to the firstcomponent (having the first circular polarization) of the secondcombined light 5716. The second component (having the second linearpolarization) of the first combined light 5712 is converted by thequarter-wave plate 5714 to the second component (having the secondcircular polarization) of the second combined light 5716.

The photonic integrated circuit 5704 includes a quarter-wave plate 5718that receives the second combined light 5716 transmitted by the circularpolarization maintaining fiber 5706, and converts the second combinedlight 5716 to third combined light 5720. The third combined light 5720includes a first component that has a first linear polarization and asecond component that has a second linear polarization, in which thesecond linear polarization is substantially orthogonal to the firstlinear polarization. The quarter-wave plate 5718 converts the firstcomponent (having the first circular polarization) of the secondcombined light 5716 to the first component (having the first linearpolarization) of the third combined light 5720. The quarter-wave plate5718 converts the second component (having the second circularpolarization) of the second combined light 5716 to the second component(having the second linear polarization) of the third combined light5720. A polarization beam splitter 5722 splits the third combined light5720 into first light having the first linear polarization and secondlight having the second linear polarization. The first light is sent toa first modulator 5724 a, and the second light is sent to a secondmodulator 5724 b.

An advantage of this design is that the circular polarizationmaintaining fiber 5706 can be mounted to the first quarter-wave plate5714 and the second quarter-wave plate 5718 at any rotational angle,reducing the alignment or packaging cost.

Referring to FIG. 58, in some implementations, an optoelectronic dataprocessing system 5800 includes an optical power supply source 5802 anda photonic integrated circuit 5806, in which a circular polarizationmaintaining fiber 5706 is optically coupled between the optical powersupply source 5802 and the photonic integrated circuit 5806. The regionbetween the optical power supply source 5802 and the photonic integratedcircuit 5806 forms a rotationally invariant region. In the optical powersupply source 5802, a quarter-wave plate 5804 is positioned between thelasers 5708 a and 5708 b and the polarization beam splitter 5710. In thephotonic integrated circuit 5806, the quarter-wave plate 5808 ispositioned between the polarization beam splitter 5722 and themodulators 5724 a and 5724 b. In this example, at the optical powersupply source 5802, the linearly polarized lights from the lasers 5708 aand 5708 b are converted to circularly polarized lights before beingcombined by the polarization beam splitter 5710. At the photonicintegrated circuit 5806, the polarization beam splitter 5722 splits thelight from the circular polarization maintaining fiber 5706 into twocircularly polarized lights, which are converted by the quarter-waveplate 5808 into two linearly polarized lights that are sent to themodulators 5724 a and 5724 b.

Referring to FIG. 59, in some implementations, an optoelectronic dataprocessing system 5900 includes an optical power supply source 5902 anda photonic integrated circuit 5906, in which a circular polarizationmaintaining fiber 5706 is optically coupled between the optical powersupply source 5902 and the photonic integrated circuit 5906. The regionbetween the optical power supply source 5902 and the photonic integratedcircuit 5906 forms a rotationally invariant region. The optical powersupply source 5902 includes a first laser 5708 a and a second laser 5708c that have the same linear polarization, i.e., the polarizationdirection of the linearly polarized light generated by the first laser5708 a is substantially parallel to the polarization direction of thelinearly polarized light generated by the second laser 5708 b. Apolarization rotator 5904 is provided to rotate the polarization of thelight output from the second laser 5708 c by 90° before being combinedwith the light from the first laser 5708 a at the polarization beamsplitter 5710.

At the photonic integrated circuit 5906, a polarization rotator 5908 isprovided to rotate the polarization of one of the light output from thepolarization beam splitter by 90° before being sent to a modulator 5724c. The modulator 5724 c and the modulator 5724 a are configured toreceive light having the same linear polarization. By comparison, in theexamples of FIGS. 57 and 58, the modulators 5724 a and 5724 b areconfigured to receive light having different linear polarizations (e.g.,polarizations that are orthogonal to each other).

Referring to FIG. 60, in some implementations, an optoelectronic dataprocessing system 6000 includes an optical power supply source 6002 anda photonic integrated circuit 6004, in which a circular polarizationmaintaining fiber 5706 is optically coupled between the optical powersupply source 6002 and the photonic integrated circuit 6004. The regionbetween the optical power supply source 6002 and the photonic integratedcircuit 6004 forms a rotationally invariant region. At the optical powersupply source 6002, a quarter-wave plate 6006 is positioned upstream ofthe polarization beam splitter 5710, and downstream of the polarizationrotator 5904 and the laser 5708 a. In the photonic integrated circuit6004, the polarization beam splitter 6008 is positioned downstream ofthe polarization beam splitter 5722, and upstream of the polarizationrotator 5908 and the modulator 5724 a.

FIG. 61 is a side view of an example of a fiber-to-PIC connector 6100that couples an input fiber array to a photonic integrated circuit. Thefiber-to-PIC connector 6100 enables horizontal fiber attachment, i.e.,at the attachment locations, the fibers extend parallel to the topsurface of the photonic integrated circuit. The diagram shows a raytracing simulation of the design using a silicon lens array for couplingto an input fiber array. The fiber-to-PIC connector 6100 enablesincoming light beams to be directed at the vertical coupling elements onthe photonic integrated circuit at an angle of incidence θ1 thatmaximizes the coupling efficiency of the vertical coupling elements. Theangle of incidence θ1 can be in a range, e.g., from 1° to 30°, 1° to16°, or 4° to 12°, or about 8°, depending on the design of the verticalcoupling elements. The vertical coupling elements can be, e.g., verticalgrating couplers. The fiber-to-PIC connector 6100 also enables outgoinglight beams to be emitted from the vertical coupling elements at theangle θ1 and be coupled to the horizontally oriented fibers of the inputfiber array.

In some implementations, the fiber-to-PIC connector 6100 includes afirst lens array 6102 having an array of lenses 6104, a birefringentbeam displacement element (or walk-off element) 6106, a birefringenthole plate 6108, a turning mirror 6110 having a reflecting surface 6124,and a second lens array 6112. The first lens array 6102 can be made of,e.g., silicon. Each lens in the array 6102 is formed by a curvedinterface to another material with different refractive index. An inputfiber array 6128 is vertically coupled to the first lens array 6102with, e.g., a 0° incidence angle. The turning mirror 6110 can be, e.g.,a glass prism block.

A light beam 6116 from an input fiber of the fiber array 6128 iscollimated by a corresponding lens 6104 in the first lens array 6102.The first lens array 6102 is attached to the birefringent beamdisplacement element 6106 using, e.g., an optical adhesive. Thebirefringent beam displacement element 6106 separates the collimatedlight beam into a first beam component 6118 that has a firstpolarization and a second beam component 1028 that has a secondpolarization. For example, the second polarization can be rotated 90°relative to the first polarization. The birefringent beam displacementelement 6106 can be made of a birefringent material, e.g., properlyoriented calcite, yttrium orthovanadate (YVO₄), or a-BBO. Thebirefringent beam displacement element 6106 separates the second beamcomponent 6120 from the first beam component 6118 by a walk-offdistance.

In some implementations, the birefringent hole plate 6108 can includeregions that have a birefringent material, and regions that haveopenings (or regions without the birefringent material), similar to thebirefringent hole plate 1006 (FIG. 13C), 1402 (FIG. 14B), 1502 (FIG.15B), 1602 (FIG. 16B), 1702 (FIG. 17B), 1802 (FIG. 18B), 1902 (FIG.19B), 2002 (FIG. 20B), 2100 (FIG. 21A), 2104 (FIG. 21B), 2108 (FIG.21C), 2116 (FIG. 21D), or 3602 (FIG. 36). In some implementations, thebirefringent hole plate 6108 can include regions that have abirefringent material, and regions that have non-birefringent opticallytransparent material, similar to the patterned birefringent plate 5004(FIG. 50) or 5104 (FIG. 51).

The first beam component 6118 passes through an opening or anon-birefringent optically transparent material in the birefringent holeplate 6108 and maintains its polarization. The second beam component6120 passes through the birefringent material of the birefringent holeplate 6108, which causes its polarization to rotate 90° and have apolarization parallel to the first beam component 6118.

The reflecting surface 6124 is at an angle θ2 relative to the plane ofthe main surface of a photonic integrated circuit 6134. The turningmirror 6110 redirects the first and second beam components 6118, 6120toward the photonic integrated circuit 6134. The angle θ2 is alsoreferred to as the turning mirror angle. The first and second beamcomponents 6118, 6120 pass through corresponding lenses of a second lensarray 6112, which focus the first and second beam components 6118 and6120 toward corresponding grating couplers 6122 (only one is shown inthe figure) at the incidence angle θ1. For example, θ2=41.2°, and θ1=8°.Depending on the design of the grating couplers 6122, the angles θ1 and02 can also be other values in order to maximize the coupling efficiencyto the grating couplers 6122.

For example, the second lens array 6112 can be made of glass. The secondlens array 6112 is attached to a lower surface 6126 of the glass prismblock of the turning mirror 6110. The lower surface 6126 is at adistance f1 from the grating couplers 6122, in which f1 is approximatelyequal to the focal distance of the lenses in the second lens array 6112.For example, the turning mirror 6110 includes one or more supportportions 6132 that define glue pockets 6132, and the turning mirror 6110is secured to the photonic integrated circuit 6134 by applying glueinside the glue pockets 6132.

The input fiber array 6128 can include a two-dimensional arrangement(e.g., two-dimensional array) of input fibers. The first lens array 6102can have a two-dimensional arrangement of lenses 6104 that correspond tothe two-dimensional arrangement of fibers in the input fiber array 6128.The photonic integrated circuit can have a two dimensional arrangement(e.g., two-dimensional array) of grating couplers. The fiber-to-PICconnector 6100 couples the light beams from at least some of the fibersof the input fiber array 6128 to at least some of the grating couplers6122 on the photonic integrated circuit 6134.

The dimensions of the first lens array 6102, the birefringent beamdisplacement element 6106, and the turning mirror 6110 depend on, e.g.,the dimensions of the input fiber array 6128, the dimensions of the areaoccupied by the grating couplers 6122, and the spacing between thegrating couplers 6122. The first lens array 6102 has a thickness of t1,and the birefringent beam displacement element 6106 has a thickness oft2. For example, t1 can be about 1.4 mm and t2 can be about 1.8 mm. Forexample, the air gap f1 can be about 0.4 mm. Increasing t1 will increasethe diameter of the collimated beam components 6118 and 6120. Increasingt2 will increase the walk-off distance between the first and second beamcomponents 6118 and 6120. The distance between a pair of gratingcouplers that receive the first and second beam components 6118, 6120 isd1. A larger d1 corresponds to a larger t2, and conversely, a smaller d1corresponds to a smaller t2.

For ease of illustration, in the example of FIG. 61, the input fibersextend along the z-direction at the location where the input fiberscouple to the first lens array 6102. For example, the input fiber array6128 includes rows and columns of fibers, in which the row directionextends along the x-direction, and the column direction extends alongthe y-direction. The dimension of the input fiber array 6128 in the ydirection is w1, which can be, e.g., 2.75 mm. The distance w1 refers tothe distance between the optical axis of a fiber core of an input fiberpositioned at the top row, and the optical axis of a fiber core of aninput fiber positioned at the bottom row. The input fiber array 6128 hasa footprint measured along a plane parallel to the x-y plane. Thegrating couplers have a footprint measured along the top surface of thephotonic integrated circuit 6134, in which the top surface is parallelto the x-z plane. For example, the dimension of the footprint of theinput fiber array 6128 in the y-direction roughly corresponds to thedimension of the footprint of the grating couplers in the z-direction,and the dimension of the footprint of the input fiber array 6128 in thex-direction roughly corresponds to the dimension of the footprint of thegrating couplers in the x-direction.

In the example of FIG. 61, the turning mirror angle (for example 41.2°)is optimized so that the light beams propagate at a non-zero anglerelative to the optical axis of the lenses of the second lens array6112, causing the light beams to be coupled to the grating couplers 6122on the photonic integrated circuit 6134 at an optimized angle of, e.g.,8°. This allows for larger beam diameters compared to using off-axisbeams in combination with conventional lenses. The birefringent beamdisplacement element 6106 can be placed at different positions in thepropagation path of the light beams. In some implementations, theturning mirror 6110 and the second lens array 6112 are made from asingle block of glass or silicon. In some examples, the second lensarray 6112 is made separately from the turning mirror 6110 and attachedto the turning mirror 6110.

FIG. 62 shows the fiber-to-PIC connector 6100 coupled between the inputfiber array 6128 and the photonic integrated circuit 6134. The figureshows the propagation paths of a first input light beam 6202 from afirst input fiber 6204, and a second input light beam 6206 from a secondinput fiber 6208. The first input fiber 6204 and the second input fiber6208 are part of the input fiber array 6128. The first input light beam6202 is separated into two beam components that are coupled to a firstpair of grating couplers 6212. The second input light beam 6206 isseparated into two beam components that are coupled to a second pair ofgrating couplers 6214. In the reverse direction, the light beams outputfrom the first pair of grating couplers 6212 are coupled to the firstinput fiber 6204, and the light beams output from the second pair ofgrating couplers 6214 are coupled to the second input fiber 6208.

FIG. 63 shows an example of a fiber-to-PIC connector 6300 coupled to aphotonic integrated circuit 6134. The fiber-to-PIC connector 6300includes a first lens array 6302 that has a two-dimensional arrangement(e.g., two-dimensional array) of glass lenses 6304. The fiber-to-PICconnector 6300 includes a birefringent beam displacement element (orwalk-off element) 6106, a birefringent hole plate 6108, a turning mirror6110, and a second lens array 6112, similar to those of the fiber-to-PICconnector 6100. An air gap 6306 is provided between the first lens array6104 and the birefringent beam displacement element 6106. The first lensarray 6104 is attached to the birefringent beam displacement element6106 through coupling elements 6308 at the edges of the first lens array6104 using, e.g., an optical adhesive. The first lens array 6104 has athickness of t3, in which t3 can be, e.g., 0.6 mm.

The figure shows the propagation paths of a first input light beam 6202from a first input fiber 6204, and a second input light beam 6206 from asecond input fiber 6208. The first input fiber 6204 and the second inputfiber 6208 are part of the input fiber array 6128. The first input lightbeam 6202 is separated into two beam components that are coupled to afirst pair of grating couplers 6212. The second input light beam 6206 isseparated into two beam components that are coupled to a second pair ofgrating couplers 6214. In the reverse direction, the light beams outputfrom the first pair of grating couplers 6212 are coupled to the firstinput fiber 6204, and the light beams output from the second pair ofgrating couplers 6214 are coupled to the second input fiber 6208.

Comparing the examples shown in FIGS. 62 and 63, one advantage ofsilicon lenses in the fiber-to-PIC connector 6100 is that glue can beused right on top of the lens because of the high refractive index ofsilicon. Because glass and glue can have a similar refractive index, theair gap is provided for the glass lenses to preserve the lensperformance. Glass lenses can have other advantages, for example,assembly becomes easier because the glass lenses are transparent tovisible light. The first lens array 6102 includes an array of smallsilicon lenses formed on a silicon block, and the first lens array 6302includes an array of small glasses lenses formed on a glass block. Thesilicon and glass blocks shown in FIGS. 62 and 63 have differentthicknesses due to different optical path lengths in materials withdifferent refractive indices. The dimensions in the figures are chosenso that the optical assembly has an approximate 1:1 magnification forimaging the fiber mode to the grating coupler on the photonic integratedcircuit.

FIG. 64 shows an example of a fiber-to-PIC connector 6400 coupledbetween an input fiber array 6128 and a photonic integrated circuit6134. The fiber-to-PIC connector 6400 includes a first lens array 6302,a turning mirror 6110, a birefringent beam displacement element 6402, abirefringent hole plate 6426, and a second lens array 6404. In thisexample, the first lens array 6302 is coupled to a first face 6406 ofthe turning mirror 6110. A second face 6408 of the turning mirror 6110is coupled to a first face 6422 of the birefringent beam displacementelement 6402. An air gap 6420 is provided between the lenses of thefirst lens array 6302 and the first face 6406 of the birefringent beamdisplacement element 6402. The birefringent beam displacement element6402 has a second face 6426 that is coupled to the birefringent holeplate 6426. The birefringent hole plate 6426 is positioned between thesecond face 6426 of the birefringent beam displacement element 6402 andthe second lens array 6404. The birefringent hole plate 6426 can includeregions that have a birefringent material, and regions that haveopenings (or regions without the birefringent material, or regions thathave non-birefringent optically transparent material) similar to thebirefringent hole plate 6108 of FIGS. 61-63.

An air gap 6418 is provided between the birefringent hole plate 6426 andthe lenses of the second lens array 6404. For example, the second lensarray 6404 includes an array of glass lenses formed on a glass block.The thickness of the glass block is t4, which can be, e.g., 0.6 mm. Forexample, the thickness of the glass block for the first lens array 6302and the thickness of the glass block for the second lens array 6404 canbe substantially the same.

For example, a first input light beam 6202 from a first input fiber 6204is redirected by the turning mirror 6110 towards the birefringent beamdisplacement element 6402, which separates the first input light beam6202 into a first beam component 6410 and a second beam component 6412.After passing the birefringent beam displacement element 6402, thesecond beam component 6412 has a polarization that is, e.g., 90°relative to the polarization of the first beam component 6410. Thebirefringent hole plate 6426 rotates the polarization of the second beamcomponent 6412 by 90°. After passing the birefringent hole plate 6426,the first and second beam components 6410, 6412 have parallelpolarization. Corresponding lenses in the second lens array 6404 focusthe first and second beam components 6410, 6412 to a first pair ofgrating couplers 6212 with an incidence angle of, e.g., 8°. A secondinput light beam 6206 from a second input fiber 6208 is redirected bythe turning mirror 6110 towards the birefringent beam displacementelement 6402, which separates the second input light beam 6206 into afirst beam component 6414 and a second beam component 6416 that have,e.g., orthogonal polarization. After passing through the birefringenthole plate 6426, the first and second beam components 6414, 6416 haveparallel polarization. Corresponding lenses in the second lens array6404 focus the first and second beam components 6414, 6416 to a secondpair of grating couplers 6214 with an incidence angle of, e.g., 8°. Thelight beams output from the first pair of grating couplers 6212 arecoupled to the first input fiber 6204, and the light beams output fromthe second pair of grating couplers 6214 are coupled to the second inputfiber 6208.

The following describes a mechanism for accurately aligning an array ofoptical fibers to a photonic integrated circuit to improve theefficiency of light coupling between the fiber array and the photonicintegrated circuit. A novel assembly approach is used in which the finalcritical alignment and bond is performed actively with a ferrule framethat is bonded to an optical subassembly stack. The ferrule frame is ahigh precision component that is the connection interface for theoptical fiber array.

FIG. 65 shows an example of a co-packaged optical module 6500 that canbe part of an optoelectronic device or system, e.g., any one of thecommunication devices 101 ₁ to 101 ₆. The co-packaged optical module6500 includes a photonic integrated circuit 6502 that hasvertical-coupling elements 6504 disposed along a main surface 6506 ofthe photonic integrated circuit 6502. The co-packaged optical module6500 includes an optical fiber to photonic integrated circuit opticalsubassembly 6508 for coupling light from an array of optical fibers 6510to the photonic integrated circuit 6502. The figure shows the opticalpath for a single beam between a single vertical-coupling element 6504and a single fiber core 6532 in the optical fiber 6510. There can bemultiple fiber cores 6532 and multiple vertical-coupling elements 6504.

In this example, the optical subassembly 6508 includes a first lensarray 6512, a beam displacer 6514, a half wave plate 6516, and a secondlens array 6518. The figure shows one of the lenses in the first lensarray 6512 and one of the lenses in the second lens array 6518.

Simulations of the coupling performance of this arrangement at 1550 nmand 1310 nm signal wavelengths show that low loss can be achieved whenthe components are accurately positioned, e.g., with sub-micronaccuracy. For different configurations of the optical fibers and theoptical subassembly, different alignment accuracies may be required. Acombination of active and passive alignment methods can be used toachieve the required alignment accuracy.

Referring to FIG. 66, the left portion of the figure shows a side viewof the co-packaged optical module 6500 that can achieve low couplingloss between the array of optical fibers 6510 and the vertical-couplingelements 6504. The right portion of the figure shows the top view ofeach component the co-packaged optical module 6500, shown in order ofposition in optical subassembly. For example, the vertical-couplingelements 6504 can be grating couplers. The figure shows one of manystack arrangements that can be used, in which different stackarrangements can have different stack components depending on theapplication.

In some embodiments, the photonic integrated circuit 6502 can be similarto the photonic integrated circuit 210 of FIG. 12, and thevertical-coupling elements 6504 can be similar to the vertical couplingelements 231. Each vertical-coupling element 6504 can include, e.g., asingle-polarization vertical grating coupler, a turning mirror, apolarization-diversity vertical grating coupler, a vertical cavitysurface emitting laser, a surface-normal modulator, a photodiode, or anycombination of the above. The second lens array 6518 can include anarray of lenses 6524. For example, the second lens array 6518 can besimilar to the lens array 541, the lens array 542, or a combination ofthe lens array 541 and the lens array 542. The half wave plate 6516 canbe similar to the birefringent hole plate 1006. For example, the halfwave plate 6516 can be made of a birefringent material with holes 6526.Light that passes through the birefringent material changes polarizationstate, whereas light that passes through the holes does not changepolarization state. The beam displacer 6514 can be similar to thewalk-off crystal 1004, which splits an incoming beam into acorresponding pair of outgoing beams that contain respective light oftwo orthogonal polarization states of the incoming beam. The first lensarray 6512 can have an array of lenses 6528, which can be similar to thelenses 551. The array of fibers 6510 can include an array of fiber cores6530, which can be similar to the cores 302 and/or 1034.

In some implementations, a light beam 6520 from a fiber core 6530 isprojected by a lens in the first lens array 6512 toward the beamdisplacer 6514, which splits the light beam into a first beam component6522 a that has “x” polarization and a second beam component 6522 b thathas “y” polarization, similar to the example shown in FIG. 12. Forexample, the “x” polarization can be TE polarization and the “y”polarization can be TM polarization. The grating couplers 6504 a and6504 b couple the first and second beam components 6522 a, 6522 b to thephotonic integrated circuit 6502. In the example in which thevertical-coupling elements 6504 include single-polarization verticalgrating couplers, the half wave plate 6516 can have a spatially-varyingbirefringence configured to transform the incident polarized light intothe grating coupler polarization state, e.g., having the polarizationstate that maximizes the coupling efficiency of the grating coupler.

As shown in FIGS. 67A and 67B, each component in the optical subassembly6508 can have 6 degrees of mechanical motion, and the various componentsmay not be entirely aligned, e.g., the end surfaces of the componentsmay not be entirely parallel to one another. In this example, there are4 optical elements between the optical fiber array 6510 and the photonicintegrated circuit 6502, each with 6 degrees of freedom which results ina large assembly space that can lead to high photonic integratedcircuit-to-fiber coupling loss. Additionally, each optical element hasfabrication tolerances which may result in loss variations. As theoptical stack is built with components bonded together, passivealignment (e.g., vision system aligning to device features or fiducials)and active alignment (e.g., measurement of coupled light from theoptical fiber to the photonic integrated circuit) can be used toposition the component before bonding. The last alignment and bondingstep may be the most critical in terms of positional and angularassembly tolerance.

FIG. 68 shows an example of a process 6540 for assembling an opticalstack 6544 that includes the photonic integrated circuit 6502, theoptical subassembly 6508, and a ferrule frame 6542. FIG. 69 shows a topview of the ferrule frame 6542. This example is a novel assemblyapproach in which the final critical alignment and bond is done activelywith the ferrule frame 6542 that is bonded to the optical subassemblystack. The ferrule frame 6542 is a high precision component that is theconnection interface for the optical fiber array 6510. The ferrule frame6542 is designed to enable the optical fiber array 6510 to be removablyattached to the ferrule frame 6542 and aligned to optimize theefficiency of light transfer between the photonic integrated circuit6502 and the fiber cores 6530.

For example, the process 6540 includes assembling the opticalsubassembly 6508, attaching the optical subassembly 6508 to the photonicintegrated circuit 6502, removably attaching the optical fiber array6510 to the ferrule frame 6542, aligning the ferrule frame 6542 to theoptical subassembly 6508 using an active alignment process, securelyattaching the ferrule frame 6542 to the optical subassembly 6508 afterthe active alignment process is completed, and removing the fiber array6510 from the ferrule frame 6542.

The process 6540 shown in FIG. 68 is suitable for assembling the opticalsubassembly 6508 using the components shown in FIG. 66. In someimplementations, the optical subassembly can have components differentfrom those shown in FIG. 66, and the process 6540 can be modifiedaccordingly.

Referring to FIG. 68, in some implementations, the process 6540 includesa first step in which a lower surface of the half wave plate 6516 isattached or bonded to the upper surface of the second lens array 6518.An arrow 6548 shows the location where glue or bonding material isplaced to firmly attach the half wave plate 6516 to the second lensarray 6518. In a second step, the lower surface of the beam displacer6514 is attached or bonded to the upper surface of the half wave plate6516. An arrow 6550 shows the location where glue or bonding material isplaced to firmly attach the beam displacer 6514 to the half wave plate6516.

In a third step, the lower surface of the first lens array 6512 isattached or bonded to the upper surface of the beam displacer 6514. Anarrow 6552 shows the location where glue or bonding material is placedto firmly attach the first lens array 6512 to the beam displacer 6514.In a fourth step, the lower surface of the second lens array 6518 isattached or bonded to the main surface (upper surface) of the photonicintegrated circuit 6502. An arrow 6554 shows the location where glue orbonding material is placed to firmly attach the second lens array 6518to the photonic integrated circuit 6502.

Steps 1 to 4 described above include steps up to the attachment of theoptical subassembly 6508 to the photonic integrated circuit 6502. Theorder of stack assembly up to step 4 can vary. For example, the bottomsurface of the first lens array 6512 can be attached to the uppersurface of the beam displacer 6514, followed by attaching the bottomsurface of the beam displacer 6514 to the upper surface of the half waveplate 6516.

In some implementations, the array of optical fibers 6510 is attached toa fiber connector 6546, which is configured to be removably attached tothe ferrule frame 6542. The process 6540 includes a fifth step in whichthe ferrule fame 6542 is positioned between the fiber connector 6546 andthe optical subassembly 6508.

In a sixth step, the fiber connector 6546 is removably attached to theferrule frame 6542 using, e.g., one or screws, or one or more clamps. Ina seventh step, the ferrule frame 6542 is placed on the opticalsubassembly 6508, and an active alignment process is used to align theferrule frame 6542 (with the fiber connector 6546 attached) relative tothe optical subassembly 6508. In some examples, the ferrule frame 6542defines an opening 6560 that is slightly larger than the outercircumference of the optical subassembly 6508. In the seventh step, theferrule frame 6542 is moved toward the photonic integrated circuit 6502with the upper portion of the optical subassembly 6508 extending intothe opening 6560 until the end surface of the fiber array 6510 contactsthe upper surface of the optical subassembly 6508. In the example shownin FIG. 68, the ferrule frame 6542 includes two screw holes 6562 thatenable two screws to secure the fiber connector 6546 to the ferruleframe 6542.

In some implementations, the active alignment process uses an opticalloopback (e.g., two grating couplers connected by an optical waveguide)on the photonic integrated circuit 6502 to enable injecting of referencelight into one fiber and collecting the looped-back light in anotherfiber. For example, the active alignment process includes providinglight from a first fiber core 6530 of the fiber array 6512 and passingthe light through the optical subassembly 6508 to a firstvertical-coupling element 6504. The light is transmitted from the firstvertical-coupling element 6504 to a second vertical-coupling element6504 through, e.g., an optical waveguide on the photonic integratedcircuit 6502. The light is transmitted from the second vertical-couplingelement 6504 through the optical subassembly 6508 to a second fiber coreof the fiber array 6512. The light received at the second fiber core ismeasured, and the position and/or orientation of the ferrule frame 6542relative to the optical subassembly 6508 is adjusted to optimize theefficiency of light transfer between the fiber cores 6530 and thephotonic integrated circuit 6502. For example, the first and secondvertical-coupling elements 6504 can be the unused transmit-gratingcouplers 2210 a and 2210 b of FIG. 22. For example, the waveguide thatoptically couples the first vertical-coupling element 6504 to the secondvertical-coupling element 6504 can be the waveguide 2212.

In an eighth step, the fiber connector 6546 is removed from the ferruleframe 6542, leaving the finished assembly stack 6544. When thecommunication devices 101 ₁ to 101 ₆ are deployed in the field, such asin a data center, the assembly stacks 6544 are ready to receive thefiber connectors 6546. This allows an operator to quickly connectoptical fiber cables to the communication devices and at the same timeaccurately align the fiber cores to achieve a high efficiency of lighttransfer between the fiber cores and the photonic integrated circuits.

Steps 5 to 7 described above include the final active alignment andbonding. The red arrows 6556 below the ferrule frame 6542 in step 7indicate the location where glue/bonding material is placed to firmlyattach the ferrule frame 6542 to the optical subassembly 6508 onceoptimal alignment is achieved. For example, the ferrule frame 6542 canbe made of glass, metal, or plastic. For example, the ferrule frame 6542can be made of a material that is transparent or semi-transparent toultra-violet (UV) light, and the ferrule frame 6542 can be bonded to theoptical subassembly 6508 using an UV-curing adhesive.

For example, in step 7, the position of the ferrule frame 6542 can beadjusted along a plane substantially parallel to the main surface 6506of the photonic integrated circuit 6502. The position of the ferruleframe 6542 can be adjusted along an x-axis relative to the main surface6506, and/or along a y-axis relative to the main surface 6506. Theferrule frame 6542 can be rotated about a z-axis relative to the mainsurface 6506. In this example, the x- and y-axes are substantiallyparallel to the main surface 6506, and the z-axis is substantiallyperpendicular to the main surface 6506.

In some implementations, adjusting the position of the ferrule frame6542 relative to the optical subassembly 6508 can include (i) adjustinga distance of an end of the fiber connector 6546 relative to the opticalsubassembly 6508, and/or (ii) adjusting a tilt angle of an end surfaceof the fiber connector 6546 relative to the optical subassembly 6508.For example, the alignment of the ferrule frame 6542 relative to theoptical subassembly 6508 can have a precision of at least 10 μmaccuracy, at least 1 μm accuracy, or at least 0.1 μm accuracy. In thiscontext, a precision of at least 0.1 μm accuracy means that when theferrule frame 6542 is bonded to the optical submodule 6508, the ferruleframe 6542 can be positioned within 0.1 μm of the optimal position thatoptimizes light transfer between the fiber cores 6530 and the photonicintegrated circuit 6502.

For example, the array of optical fibers can include at least 10 fibercores, at least 50 fiber cores, or at least 100 fiber cores. Because thefiber cores are densely packed together, accurate alignment of the fibercores relative to the optical subassembly 6508 is important forachieving high efficiency of light transfer between the fiber cores andthe photonic integrated circuit 6502.

The mechanism that enables the fiber connector 6546 to be removablyconnected to the ferrule frame 6542 is made with high precision. In theexample in which the fiber connector 6546 is removably connected to theferrule frame 6542 using screws, the screws and the screw holes are madewith high precision so that the fiber connector 6546 can be attached tothe ferrule frame 6542 with a precision in a range of, e.g., 10 nm, or100 nm, or 1 μm. In this context, a precision of 10 nm means that eachtime the fiber connector 6546 is removably attached to the ferrule frame6542, the position of the fiber connector 6546 will be consistentlywithin 10 nm relative to the optimal position of the fiber connector6546 determined by the active alignment process in step 7 of the process6540.

In some implementations, the fiber connector 6546 includes the firstlens array 6512. In this example, the optical subassembly 6508 includesthe beam displacer 6514, the half wave plate 6516, and the second lensarray 6518.

FIGS. 46A, 46B, and 48 show examples in which the fiber array (e.g.,4604, 4802) has end facets polished at an angle of, e.g., about 8°. Inthese examples, the lenses (e.g., 4604, 4608, 4610, 4622, 4624) areadapted such that the fiber-to-PIC connector outputs light beams to thefiber array at the proper angle compatible with the bevel end facets ofthe fiber array. The following describes a beveled fiber array ferruleadapter that can be used to adapt between any combination of dissimilarbevels between a fiber array connector and an optical assembly.

MPO connectors are commonly used for mating fiber cable connectors tofiber array cable connectors. The connector end faces of both connectorferrules can be beveled to lower optical back reflections from the fiberend faces.

FIG. 70 is a diagram of an example beveled fiber array ferrule adapter7000 coupled between a beveled MPO-like fiber array ferrule of anMPO-like fiber connector 7002 and an optical assembly 7004. The MPO-likefiber connector 7002 is connected to a plurality of optical fibers 7024.The optical assembly 7004 can include, e.g., a photonic integratedcircuit 7010 and a fiber-to-PIC connector 7012 described above. Forexample, the fiber-to-PIC connector 7012 can include a first lens array7014, a birefringent beam displacement element 7016, and a second lensarray 7018. The optical assembly 7004 can generate output optical beamsto and receive input optical beams from the MPO-like fiber connector7002 through the beveled fiber array ferrule adapter 7004.

The MPO-like fiber connector 7002 has an end 7006 that is beveled, andthe beveled fiber array ferrule adapter 7000 has an end 7008 that isalso beveled to the same angle as the end 7006 of the MPO-like fiberconnector ferrule. The beveled fiber array ferrule adapter 7000 can bemade as nominally the same ferrule type as the MPO-like fiber connector7002 in which optical fibers are inserted in the ferrule holes andpolished down to be nominally flush on the both optical faces of thebeveled fiber array ferrule adapter 7000. The beveled fiber arrayferrule adapter 7000 enables a low-loss connection between the MPO-likefiber connector 7002 and the optical assembly 7004 whose mating surfaceis not beveled at the correct angle to directly mate to the MPO-likefiber connector 7002. In some implementations, the fiber array ferruleadapter 7000 is permanently bonded to the optical subassembly 7004 atthe interface 7020.

An MPO-like connector has optical fibers that are inserted in theferrule holes and polished down to be nominally flush on the opticalface of the MPO-like connector, similar to those of a standard MPOconnector. The MPO-like connector can have alignment pins or holessimilar to those of a standard MPO connector. The cross-sectionalprofile of the MPO-like connector ferrule can be different from that ofthe standard MPO connector in order to accommodate various arrangementsof optical fibers. For example, an MPO-like connector can be used toconnect to an optical fiber cable having a two-dimensional arrangementof optical fibers, such as a two-dimensional array of optical fibers.The two-dimensional array of optical fibers can have multiple rows andmultiple columns of optical fibers, e.g., at least 2 rows and at least 4columns of optical fibers, or at least 2 rows and at least 8 columns ofoptical fibers, or at least 3 rows and at least 8 columns of opticalfibers.

The beveled fiber array ferrule adapter 7000 can also be configured tobe coupled between a beveled MPO fiber array ferrule of a standard MPOfiber connector and an optical assembly whose output light beams areconfigured to be compatible with a standard MPO fiber connector.

While the figure shows the optical assembly 7004 with a 0° bevel opticalface, the fiber array ferrule adapter 7000 can be used to adapt betweenany combination of dissimilar bevels between a fiber array connector(e.g., 7002) and an optical assembly (e.g., 7004).

In some examples, the fiber array ferrule adapter 7000 is a maleconnector that has alignment pins 7022 that are mated with alignmentholes in the beveled MPO connector 7002. In some examples, the MPOconnector 7002 is a male connector that has alignment pints 7022 thatare mated with alignment holes in the beveled fiber array ferruleadapter 7000. The interface of the fiber array ferrule adapter 7000 canhave a configuration similar to a conventional ferrule-to-ferruleconnector such that the fiber array ferrule adapter 7000 can be matedwith a standard MPO connector or an MPO-like connector.

In some implementations, a laser source that is configured generatecircularly polarized light can be used in the examples shown in FIGS. 27and 54 to 60 without the need to use the quarter-wave plate or thequarter-wave polarization rotator.

In an example, a first system includes a data processor configured toprocess data, and a photonic integrated circuit configured to convertoptical signals received from one or more optical fibers to electricalsignals that are transmitted to the data processor.

In an example, a second system includes a data processor configured toprocess data, and a photonic integrated circuit configured to convertelectronic signals from the data processor to optical signals that canbe output to one or more optical fibers.

In an example, a third system includes a data processor configured toprocess data, and a photonic integrated circuit configured to convertoptical signals received from one or more optical fibers to electricalsignals that are transmitted to the data processor. The photonicintegrated circuit is also configured to convert electronic signals fromthe data processor to optical signals that can be output to the one ormore optical fibers.

In some implementations, each of the first, second, and third systemscan include a fiber-to-PIC connector that is optically coupled to theone or more optical fibers, and also optically coupled to couplingelements of the photonic integrated circuit. The coupling elements canbe, e.g., grating couplers or edge couplers. The fiber-to-PIC connectorcan include one or more of the features described above, such as one ormore features of the fiber-to-PIC connector arrangement 500 of FIG. 5,the fiber-to-PIC connector arrangement 600 of FIG. 6, the fiber-to-PICconnector arrangement 700 of FIG. 7, fiber-to-PIC connector 900 of FIG.9, the fiber-to-PIC connector 1000 of FIGS. 10A, 10B, 12, 13, thefiber-to-PIC connector 1100 of FIG. 11A, the fiber-to-PIC connector 2300of FIG. 23, the fiber-to-PIC connector 2400 of FIG. 24A, 24B, thefiber-to-PIC connector 2800 of FIG. 28, the fiber-to-PIC connector 3310of FIG. 33C, the fiber-to-PIC connector 3400 of FIG. 34A, 34B, thefiber-to-PIC connector 3500 of FIG. 35, the fiber-to-PIC connector 3800of FIG. 38, the fiber-to-PIC connector 3900 of FIG. 39, and thefiber-to-PIC connector 4000 of FIG. 40.

Each of the first, second, and third systems can include one or morefeatures or components described in U.S. patent application Ser. No.16/822,103, filed on Mar. 18, 2020, U.S. patent application Ser. No.16/847,705, filed on Apr. 14, 2020, U.S. patent application Ser. No.16/888,890, filed on Jun. 1, 2020, U.S. provisional patent application63/080,528, filed on Sep. 18, 2020, U.S. provisional patent application63/088,914, filed on Oct. 7, 2020, U.S. provisional patent application63/116,660, filed on Nov. 20, 2020, and U.S. provisional patentapplication 63/146,421, filed on Feb. 5, 2021. The entire contents ofthe above applications are incorporated by reference.

It should be appreciated by those of ordinary skill in the pertinent artthat at least some embodiments described herein in the context ofcoupling light from one or more fibers 202 to PIC 210 can be equallyoperable to couple light from PIC 210 to one or more fibers 202. Thisreversibility of the coupling direction is a general feature of at leastsome embodiments described herein, including some of those usingpolarization diversity.

Example optical systems disclosed herein should only be viewed as someof many possible embodiments that can be used to perform polarizationdemultiplexing and independent array pattern scaling, array geometryre-arrangement, spot size scaling, and angle-of-incidence adaptationusing diffractive, refractive, reflective, and polarization-dependentoptical elements, 3D waveguides and 3D printed optical components. Otherimplementations achieving a similar set of functionalities can be madeand used by persons of ordinary skill in the pertinent art, in view ofthis disclosure and without any undue experimentation.

According to an example embodiment disclosed above, e.g., in the summarysection and/or in reference to any one or any combination of some or allof FIGS. 1-8, provided is an apparatus comprising: one or more opticalfibers (e.g., 202, FIG. 5) having a plurality of fiber cores (e.g., 302,FIGS. 3A-3G); a photonic integrated circuit (e.g., 210, FIG. 5)including a plurality (e.g., 230, FIG. 5) of vertical-coupling elements(e.g., 231, FIG. 5) disposed along a main surface of the photonicintegrated circuit; and a fiber-optic connector (e.g., 240/250, FIG. 5)connected between the one or more optical fibers and the photonicintegrated circuit to communicate light therebetween through the mainsurface, the fiber-optic connector comprising optics configured totransfer light between the plurality of fiber cores and the plurality ofvertical-coupling elements such that: a distance (e.g., S_(min), FIGS.3A-3G) between a first pair of the fiber cores is optically scaled by afirst scaling factor (e.g., A); and a diameter (e.g., D_(core), FIGS.3A-3G) of at least one of the fiber cores is optically scaled by asecond scaling factor (e.g., C₁) that is different from the firstscaling factor.

In some embodiments of the above apparatus, the optics is furtherconfigured to transfer the light such that a distance (e.g., S_(max),FIGS. 3A-3G) between a second pair of the fiber cores is opticallyscaled by a third scaling factor (e.g., B) that is different from thesecond scaling factor.

In some embodiments of any of the above apparatus, the optics isconfigured to transfer the light such that the third scaling factor isdifferent from the first scaling factor.

In some embodiments of any of the above apparatus, the optics isconfigured to transfer the light such that the first scaling factor issubstantially equal to the third scaling factor.

In some embodiments of any of the above apparatus, the optics comprises:one or more first lenses (e.g., 551, FIG. 5) located at a first offsetdistance from the main surface; a plurality of second lenses (e.g., 541,FIG. 5) located at a second offset distance from the main surface, thesecond offset distance being smaller than the first offset distance; anda plurality of third lenses (e.g., 542, FIG. 5) located at a thirdoffset distance from the main surface, the third offset distance beingsmaller than the second offset distance.

In some embodiments of any of the above apparatus, the optics comprisesat least one lens (e.g., 542, FIG. 5) configured to communicate lightwith a single one of the fiber cores and a single one of thevertical-coupling elements.

In some embodiments of any of the above apparatus, the optics comprisesa plurality of optical waveguides (e.g., 652, FIG. 6), each opticallyconnecting a respective one of the fiber cores and a respective one ofthe vertical-coupling elements.

In some embodiments of any of the above apparatus, at least some of theoptical waveguides are tapered.

In some embodiments of any of the above apparatus, the optics comprisesone or more polarization beam splitters (e.g., 810 and 820, FIG. 8A andFIG. 8B).

In some embodiments of any of the above apparatus, the optics comprisesone or more polarization-rotating elements (e.g., 861, 862, FIG. 8B).

In some embodiments of any of the above apparatus, the fiber-opticconnector comprises a first connector part (e.g., 250, FIG. 5) and asecond connector part (e.g., 240, FIG. 5) disconnectably connected toone another.

In some embodiments of any of the above apparatus, the optics isconfigured to produce, at a mating surface between the first and secondconnector parts, light spots (e.g., 560, FIG. 5) of a larger size, by atleast a factor of two, than corresponding diameters of the fiber cores.

In some embodiments of any of the above apparatus, the optics isconfigured to communicate light between a first number of the fibercores and a second number of the vertical-coupling elements, the secondnumber being greater than the first number.

In some embodiments of any of the above apparatus, the one or moreoptical fibers include a multi-core optical fiber.

In some embodiments of any of the above apparatus, each of thevertical-coupling elements is selected from an element set consistingof: a single-polarization vertical grating coupler, a turning mirror, apolarization-diversity vertical grating coupler, a vertical cavitysurface emitting laser, a surface-normal modulator, and a photodiode.

According to another example embodiment disclosed above, e.g., in thesummary section and/or in reference to any one or any combination ofsome or all of FIGS. 1-8, provided is a fiber-optic connectorcomprising: a first connector part (e.g., 240, FIG. 5) connectable at afirst side thereof (e.g., 555, FIG. 5) to one or more optical fibers(e.g., 202, FIG. 5) having a plurality of fiber cores (e.g., 302, FIGS.3A-3G), the first connector part having a second side that is oppositeto the first side (e.g., 556, FIG. 5); a second connector part (e.g.,250, FIG. 5) connectable at one side thereof (e.g., 545, FIG. 5) to thesecond side of the first connector part and further connectable at anopposite side thereof (e.g., 546, FIG. 5) to a photonic integratedcircuit (e.g., 210, FIG. 2); and optics configured to transfer lightbetween the first side of the first connector part and the opposite sideof the second connector part such that: a distance (e.g., S_(min), FIGS.3A-3G) between a first pair of the fiber cores is optically scaled by afirst scaling factor (e.g., A); and a diameter (e.g., D_(core), FIGS.3A-3G) of at least one of the fiber cores is optically scaled by asecond scaling factor (e.g., C₁) that is different from the firstscaling factor.

As used herein, the term “opposite” refers to a relative orientationand/or position of two corresponding sides or edges of the part andshould be construed to cover any of the relative orientations/positionsin which: (i) such two sides are substantially (e.g., to within 15degrees) parallel to one another but located at different ends of thepart; (ii) such two sides are not parallel to one another, i.e., can beoriented at a relative angle in the range between 15 degrees and 165degrees; (iii) such two sides are substantially perpendicular to oneanother; (iv) at least one of such two sides is not strictly planar andhas some features deviating from the planar geometry; (v) such two sideshave no point of contact with one another; and (vi) such two sides havea common edge or area of contact, e.g., at the corner of the part. Thesides 545, 546, 555, and 556 shown in FIG. 5 should be viewed asproviding non-limiting illustrative examples of such sides.

In some embodiments of the above fiber-optic connector, the optics isfurther configured to transfer the light such that a distance (e.g.,S_(max), FIGS. 3A-3G) between a second pair of the fiber cores isoptically scaled by a third scaling factor (e.g., B) that is differentfrom the second scaling factor.

In some embodiments of any of the above fiber-optic connectors, theoptics is configured to transfer the light such that the third scalingfactor is different from the first scaling factor.

In some embodiments of any of the above fiber-optic connectors, theoptics is configured to transfer the light such that the first scalingfactor is substantially equal to the third scaling factor.

In some embodiments of any of the above fiber-optic connectors, theoptics comprises: one or more first lenses (e.g., 551, FIG. 5) locatedat a first offset distance from the opposite side of the secondconnector part; a plurality of second lenses (e.g., 541, FIG. 5) locatedat a second offset distance from the opposite side of the secondconnector part, the second offset distance being smaller than the firstoffset distance; and a plurality of third lenses (e.g., 542, FIG. 5)located at a third offset distance from the opposite side of the secondconnector part, the third offset distance being smaller than the secondoffset distance, said first, second, and third distances being measuredwith the first and second connector parts being connected to oneanother.

In some embodiments of any of the above fiber-optic connectors, theoptics comprises at least one lens (e.g., 542, FIG. 5) configured tocommunicate light with a single one of the fiber cores and a single oneof vertical-coupling elements of the photonic integrated circuit.

In some embodiments of any of the above fiber-optic connectors, theoptics comprises a plurality of optical waveguides (e.g., 652, FIG. 6),each disposed to optically connect a respective one of the fiber coresand a respective one of vertical-coupling elements of the photonicintegrated circuit.

In some embodiments of any of the above fiber-optic connectors, at leastsome of the optical waveguides are tapered.

In some embodiments of any of the above fiber-optic connectors, theoptics comprises one or more polarization beam splitters (e.g., 810 and820, FIG. 8A and FIG. 8B).

In some embodiments of any of the above fiber-optic connectors, theoptics comprises one or more polarization-rotating elements (e.g., 861,862, FIG. 8B).

While this disclosure includes references to illustrative embodiments,this specification is not intended to be construed in a limiting sense.Various modifications of the described embodiments, as well as otherembodiments within the scope of the disclosure, which are apparent topersons skilled in the art to which the disclosure pertains are deemedto lie within the principle and scope of the disclosure, e.g., asexpressed in the following claims.

Unless explicitly stated otherwise, each numerical value and rangeshould be interpreted as being approximate as if the word “about” or“approximately” preceded the value or range.

It will be further understood that various changes in the details,materials, and arrangements of the parts which have been described andillustrated in order to explain the nature of this disclosure can bemade by those skilled in the art without departing from the scope of thedisclosure, e.g., as expressed in the following claims.

The use of figure numbers and/or figure reference labels in the claimsis intended to identify one or more possible embodiments of the claimedsubject matter in order to facilitate the interpretation of the claims.Such use is not to be construed as necessarily limiting the scope ofthose claims to the embodiments shown in the corresponding figures.

Although the elements in the following method claims, if any, arerecited in a particular sequence with corresponding labeling, unless theclaim recitations otherwise imply a particular sequence for implementingsome or all of those elements, those elements are not necessarilyintended to be limited to being implemented in that particular sequence.

Reference herein to “one embodiment” or “an embodiment” means that aparticular feature, structure, or characteristic described in connectionwith the embodiment can be included in at least one embodiment of thedisclosure. The appearances of the phrase “in one embodiment” in variousplaces in the specification are not necessarily all referring to thesame embodiment, nor are separate or alternative embodiments necessarilymutually exclusive of other embodiments. The same applies to the term“implementation.”

Unless otherwise specified herein, the use of the ordinal adjectives“first,” “second,” “third,” etc., to refer to an object of a pluralityof like objects merely indicates that different instances of such likeobjects are being referred to, and is not intended to imply that thelike objects so referred-to have to be in a corresponding order orsequence, either temporally, spatially, in ranking, or in any othermanner.

Also for purposes of this description, the terms “couple,” “coupling,”“coupled,” “connect,” “connecting,” or “connected” refer to any mannerknown in the art or later developed in which energy is allowed to betransferred between two or more elements, and the interposition of oneor more additional elements is contemplated, although not required.Conversely, the terms “directly coupled,” “directly connected,” etc.,imply the absence of such additional elements.

The description and drawings merely illustrate the principles of thedisclosure. It will thus be appreciated that those of ordinary skill inthe art will be able to devise various arrangements that, although notexplicitly described or shown herein, embody the principles of thedisclosure and are included within its spirit and scope. Furthermore,all examples recited herein are principally intended expressly to beonly for pedagogical purposes to aid the reader in understanding theprinciples of the disclosure and the concepts contributed by theinventor(s) to furthering the art, and are to be construed as beingwithout limitation to such specifically recited examples and conditions.Moreover, all statements herein reciting principles, aspects, andembodiments of the disclosure, as well as specific examples thereof, areintended to encompass equivalents thereof.

As used in this application, the term “circuitry” can refer to one ormore or all of the following: (a) hardware-only circuit implementations(such as implementations in only analog and/or digital circuitry); (b)combinations of hardware circuits and software, such as (as applicable):(i) a combination of analog and/or digital hardware circuit(s) withsoftware/firmware and (ii) any portions of hardware processor(s) withsoftware (including digital signal processor(s)), software, andmemory(ies) that work together to cause an apparatus, such as a mobilephone or server, to perform various functions); and (c) hardwarecircuit(s) and or processor(s), such as a microprocessor(s) or a portionof a microprocessor(s), that requires software (e.g., firmware) foroperation, but the software may not be present when it is not needed foroperation.” This definition of circuitry applies to all uses of thisterm in this application, including in any claims. As a further example,as used in this application, the term circuitry also covers animplementation of merely a hardware circuit or processor (or multipleprocessors) or portion of a hardware circuit or processor and its (ortheir) accompanying software and/or firmware. The term circuitry alsocovers, for example and if applicable to the particular claim element, abaseband integrated circuit or processor integrated circuit for a mobiledevice or a similar integrated circuit in server, a cellular networkdevice, or other computing or network device.

It should be appreciated by those of ordinary skill in the art that anyblock diagrams herein represent conceptual views of illustrativecircuitry embodying the principles of the disclosure.

Although the present invention is defined in the attached claims, itshould be understood that the present invention can also be defined inaccordance with the following sets of embodiments:

First Set of Embodiments:

Embodiment 1: An apparatus comprising:

-   -   one or more optical fibers having a plurality of fiber cores;    -   a photonic integrated circuit including a plurality of        vertical-coupling elements disposed along a main surface of the        photonic integrated circuit; and    -   a fiber-optic connector connected between the one or more        optical fibers and the photonic integrated circuit to        communicate light therebetween through the main surface, the        fiber-optic connector comprising optics configured to transfer        light between the plurality of fiber cores and the plurality of        vertical-coupling elements such that:        -   a distance between a first pair of the fiber cores is            optically scaled by a first scaling factor; and        -   a diameter of at least one of the fiber cores is optically            scaled by a second scaling factor that is different from the            first scaling factor.

Embodiment 2: The apparatus of embodiment 1, wherein the optics isfurther configured to transfer the light such that a distance between asecond pair of the fiber cores is optically scaled by a third scalingfactor that is different from the second scaling factor.

Embodiment 3: The apparatus of embodiment 1, wherein the opticscomprises:

-   -   one or more first lenses located at a first offset distance from        the main surface;    -   a plurality of second lenses located at a second offset distance        from the main surface, the second offset distance being smaller        than the first offset distance; and    -   a plurality of third lenses located at a third offset distance        from the main surface, the third offset distance being smaller        than the second offset distance.

Embodiment 4: The apparatus of embodiment 1, wherein the opticscomprises at least one lens configured to communicate light with asingle one of the fiber cores and a single one of the vertical-couplingelements.

Embodiment 5: The apparatus of embodiment 1, wherein the opticscomprises a plurality of optical waveguides, each optically connecting arespective one of the fiber cores and a respective one of thevertical-coupling elements.

Embodiment 6: The apparatus of embodiment 5, wherein at least some ofthe optical waveguides are tapered.

Embodiment 7: The apparatus of embodiment 1, wherein the opticscomprises one or more polarization beam splitters.

Embodiment 8: The apparatus of embodiment 1, wherein the opticscomprises one or more polarization-rotating elements.

Embodiment 9: The apparatus of embodiment 1, wherein the fiber-opticconnector comprises a first connector part and a second connector partdisconnectably connected to one another.

Embodiment 10: The apparatus of embodiment 9, wherein the optics isconfigured to produce, at a mating surface between the first and secondconnector parts, light spots of a larger size, by at least a factor oftwo, than corresponding diameters of the fiber cores.

Embodiment 11: The apparatus of embodiment 1, wherein the optics isconfigured to communicate light between a first number of the fibercores and a second number of the vertical-coupling elements, the secondnumber being greater than the first number.

Embodiment 12: The apparatus of embodiment 1, wherein each of thevertical-coupling elements is selected from an element set consistingof: a single-polarization vertical grating coupler, a turning mirror, apolarization-diversity vertical grating coupler, a vertical cavitysurface emitting laser, a surface-normal modulator, and a photodiode.

Embodiment 13: A fiber-optic connector comprising:

-   -   a first connector part connectable at a first side thereof to        one or more optical fibers having a plurality of fiber cores,        the first connector part having a second side that is opposite        to the first side;    -   a second connector part connectable at one side thereof to the        second side of the first connector part and further connectable        at an opposite side thereof to a photonic integrated circuit;        and    -   optics configured to transfer light between the first side of        the first connector part and the opposite side of the second        connector part such that:        -   a distance between a first pair of the fiber cores is            optically scaled by a first scaling factor; and        -   a diameter of at least one of the fiber cores is optically            scaled by a second scaling factor that is different from the            first scaling factor.

Embodiment 14: The fiber-optic connector of embodiment 13, wherein theoptics is further configured to transfer the light such that a distancebetween a second pair of the fiber cores is optically scaled by a thirdscaling factor that is different from the second scaling factor.

Embodiment 15: The fiber-optic connector of embodiment 13, wherein theoptics comprises:

-   -   one or more first lenses located at a first offset distance from        the opposite side of the second connector part;    -   a plurality of second lenses located at a second offset distance        from the opposite side of the second connector part, the second        offset distance being smaller than the first offset distance;        and    -   a plurality of third lenses located at a third offset distance        from the opposite side of the second connector part, the third        offset distance being smaller than the second offset distance,        said first, second, and third distances being measured with the        first and second connector parts being connected to one another.

Embodiment 16: The fiber-optic connector of embodiment 13, wherein theoptics comprises at least one lens configured to communicate light witha single one of the fiber cores and a single one of vertical-couplingelements of the photonic integrated circuit.

Embodiment 17: The fiber-optic connector of embodiment 13, wherein theoptics comprises a plurality of optical waveguides, each disposed tooptically connect a respective one of the fiber cores and a respectiveone of vertical-coupling elements of the photonic integrated circuit.

Embodiment 18: The fiber-optic connector of embodiment 17, wherein atleast some of the optical waveguides are tapered.

Embodiment 19: The fiber-optic connector of embodiment 13, wherein theoptics comprises one or more polarization beam splitters.

Embodiment 20: The fiber-optic connector of embodiment 13, wherein theoptics comprises one or more polarization-rotating elements.

Embodiment 21: The apparatus of embodiment 1 in which the fiber-opticconnector comprises a birefringent plate having holes.

Embodiment 22: The apparatus of embodiment 21 in which the holescomprise at least one of circular holes, square holes, rectangularholes, or strip holes.

Embodiment 23: The apparatus of embodiment 21 in which the birefringentplate comprises a half-wave plate.

Embodiment 24: The apparatus of embodiment 1 in which the fiber-opticconnector comprises multiple strip platelets spaced apart from eachother, in which the strip platelets are configured to rotate apolarization of optical beam components having a first polarizationstate, and the space between the strip platelets allows optical beamcomponents having a second polarization state to pass through withoutrotation of polarization.

Embodiment 25: The apparatus of embodiment 8 in which the one or morepolarization-rotating elements are implemented as a birefringent platehaving holes.

Embodiment 26: The apparatus of embodiment 1 in which the fiber-opticconnector comprises:

-   -   one or more walk-off elements configured to receive input        optical beams from one or more of the fiber cores, and separate        each input optical beam into a first optical beam component        having a first polarization and a second optical beam component        having a second polarization, and    -   a birefringent plate having holes, in which the birefringent        plate is positioned relative to the one or more walk-off        elements such that each hole is aligned with a corresponding        first optical beam component, wherein the birefringent plate        rotates a polarization of each of the second optical beam        components to cause the second optical beam component to have a        same polarization as the corresponding first optical beam        component.

Embodiment 27: The apparatus of embodiment 26 in which each of the firstand second optical beam components is directed towards one of thevertical-coupling elements.

Embodiment 28: The apparatus of embodiment 26 in which the fiber coresare configured to transmit single wavelength signals, and the number ofvertical-coupling elements for transferring input light from thefiber-optic connector to the photonic integrated circuit is twice thenumber of fiber cores that provide the input optical beams.

Embodiment 29: The apparatus of embodiment 26 in which the fiber coresare arranged in one or more rows,

-   -   wherein each walk-off element is configured to allow the first        optical beam component to pass through without displacement, and        cause the second optical beam component to be displaced at a        distance relative to the first optical beam component,    -   wherein the second optical beam is displaced in a walk-off        direction that is parallel to a row direction.

Embodiment 30: The apparatus of embodiment 26 in which the fiber coresare arranged in one or more rows,

-   -   wherein each walk-off element is configured to allow the first        optical beam component to pass through without displacement, and        cause the second optical beam component to be displaced at a        distance relative to the first optical beam component,    -   wherein the second optical beam is displaced in a walk-off        direction that is perpendicular to a row direction.

Embodiment 31: The apparatus of embodiment 26 in which each walk-offelement is configured to allow the first optical beam component to passthrough without displacement, and cause the second optical beamcomponent to be displaced at a distance relative to the first opticalbeam component,

-   -   wherein the vertical-coupling elements are configured to couple        optical signals that have electric fields along a first        direction with maximum efficiency,    -   wherein the second optical beam is displaced relative to the        first optical beam in a walk-off direction that is parallel to        the first direction.

Embodiment 32: The apparatus of embodiment 31 in which the fiber coresare arranged in one or more rows, and the first direction isperpendicular to the row direction.

Embodiment 33: The apparatus of embodiment 31 in which the fiber coresare arranged in one or more rows, the first direction is at an anglerelative to the row direction, and the angle is in a range from 100 to80°.

Embodiment 34: The apparatus of embodiment 26 in which each walk-offelement is configured to allow the first optical beam component to passthrough without displacement, and cause the second optical beamcomponent to be displaced at a distance relative to the first opticalbeam component,

-   -   wherein the vertical-coupling elements are configured to couple        optical signals that have electric fields along a first        direction with maximum efficiency,    -   wherein the second optical beam is displaced relative to the        first optical beam in a walk-off direction that is perpendicular        to the first direction.

Embodiment 35: The apparatus of embodiment 34 in which the fiber coresare arranged in one or more rows, and the first direction is parallel tothe row direction.

Embodiment 36: The apparatus of embodiment 34 in which the fiber coresare arranged in one or more rows, and the first direction is at an anglerelative to the row direction, and the angle is in a range from 10° to80°.

Embodiment 37: The apparatus of embodiment 1 in which thevertical-coupling elements comprise a first set of vertical-couplingelements that transfer light between the plurality of fiber cores andthe photonic integrated circuit, and a second set of vertical-couplingelements that do not transfer light between the plurality of fiber coresand the photonic integrated circuit,

-   -   wherein at least one pair of vertical-coupling elements in the        second set of vertical-coupling elements are connected by an        alignment waveguide that enables active alignment of the        vertical-coupling elements and the fiber-optic connector.

Embodiment 38: The apparatus of embodiment 37 in which the verticalcoupling elements are located within an overall rectangular footprint,and the second set of vertical-coupling elements is positioned withinthe overall rectangular footprint.

Embodiment 39: The apparatus of embodiment 1 in which the fiber-opticconnector comprises an optical power supply fiber port that isconfigured to receive a first optical power supply beam from an opticalfiber, wherein the fiber-optic connector comprises a first polarizationbeam splitter that is configured to split the first optical power supplybeam into a second optical power supply beam and a third optical powersupply beam.

Embodiment 40: The apparatus of embodiment 39 in which the fiber-opticconnector comprises a polarization-rotating element that rotates apolarization direction of the second optical power supply beam or thethird optical power supply beam to cause the second and third opticalpower supply beam to have the same polarization.

Embodiment 41: The apparatus of embodiment 39 in which the fiber-opticconnector comprises a second polarization beam splitter that isconfigured to split the second and third optical power supply beams intofour optical power supply beams.

Embodiment 42: The apparatus of embodiment 41 in which the firstpolarization beam splitter has a first walk-off direction, and thesecond polarization beam splitter has a second walk-off direction thatis different from the first walk-off direction.

Embodiment 43: The apparatus of embodiment 41 in which the fiber-opticconnector comprises a third polarization beam splitter that isconfigured to split the four optical power supply beams into eightoptical power supply beams.

Embodiment 44: The apparatus of embodiment 1 in which the fiber-opticconnector comprises a wavelength division multiplexer that multiplexestwo or more optical signal that have two or more different wavelengthsinto a single WDM output optical signal.

Embodiment 45: The apparatus of embodiment 44 in which the wavelengthdivision multiplexer comprises a first walk-off element and abirefringent hole plate.

Embodiment 46: The apparatus of embodiment 45 in which the wavelengthdivision multiplexer comprises a second walk-off element and awaveplate, wherein the waveplate is configured to preserve polarizationof light having a first wavelength and rotate polarization of light havea second wavelength.

Embodiment 47: The apparatus of embodiment 46 in which the waveplate isconfigured to rotate polarization of light having a third wavelength andpreserve polarization of light having a fourth wavelength, in which thefirst, second, third, and fourth wavelengths are all different from oneanother.

Embodiment 48: The apparatus of embodiment 47 in which the firstwavelength is smaller than the second wavelength, the second wavelengthis smaller than the third wavelength, and the third wavelength issmaller than the fourth wavelength.

Embodiment 49: The apparatus of embodiment 46 in which the birefringenthole plate comprises quartz, and the waveplate comprises yttriumorthovanadate (YVO₄).

Embodiment 50: The apparatus of embodiment 44 in which the wavelengthdivision multiplexer is configured to multiplex light have wavelengthscompatible with 200GBASE-FR4 wavelength-division-multiplexed laneassignments.

Embodiment 51: The apparatus of embodiment 44 in which the wavelengthdivision multiplexer is configured to multiplex light have wavelengthscompatible with 200GBASE-LR4 wavelength-division-multiplexed laneassignments.

Embodiment 52: The apparatus of embodiment 44 in which the wavelengthdivision multiplexer is configured to multiplex light have wavelengthscompatible with 400GBASE-FR8 wavelength-division-multiplexed laneassignments.

Embodiment 53: The apparatus of embodiment 7, wherein the opticscomprises one or more polarization-rotating elements, wherein thepolarization beam splitter and the polarization-rotating element arealigned along a direction substantially parallel to a top surface of thephotonic integrated circuit, wherein the fiber-optic connector comprisesa turning mirror to redirect light from the polarization-rotatingelement toward the vertical-coupling element.

Embodiment 54: The apparatus of embodiment 7, wherein the opticscomprises one or more polarization-rotating elements, wherein thepolarization beam splitter and the polarization-rotating element arealigned along a direction substantially perpendicular to a top surfaceof the photonic integrated circuit.

Embodiment 55: The apparatus of embodiment 7, wherein the opticscomprises one or more polarization-rotating elements, wherein thepolarization beam splitter and the polarization-rotating element areconfigured to enable edge coupling of light from the plurality of fibercores to the photonic integrated circuit.

Embodiment 56: The apparatus of embodiment 1 in which the fiber-opticconnector comprises a wavelength division demultiplexer that includesone or more wavelength dependent filters.

Embodiment 57: The apparatus of embodiment 56 in which the wavelengthdivision demultiplexer is configured to direct light having a firstwavelength to a first set of one or more grating couplers, and directlight having a second wavelength to a second set of one or more gratingcouplers.

Embodiment 58: The apparatus of embodiment 56 in which the wavelengthdivision demultiplexer is configured to convert K rows of N fibers to anN×2MK array of grating couplers, K, N, and M are positive integers, andM represents the number of wavelengths that is processed by thewavelength division demultiplexer.

Embodiment 59: The apparatus of embodiment 1 in which the fiber-opticconnector comprises a wavelength division multiplexer that includes oneor more wavelength dependent filters.

Embodiment 60: The apparatus of embodiment 59 in which the wavelengthdivision multiplexer is configured to combine light having a firstwavelength from a first set of one or more grating couplers and lighthaving a second wavelength from a second set of one or more gratingcouplers into a combined optical beam.

Embodiment 61: The apparatus of embodiment 59 in which the wavelengthdivision multiplexer is configured to convert an N×2MK array of gratingcouplers into K rows of N fibers, K, N, and M are positive integers, andM represents the number of wavelengths that is processed by thewavelength division multiplexer.

Embodiment 62: The apparatus of embodiment 1 in which the fiber-opticconnector comprises a wavelength division demultiplexer that includesone or more broadband optical splitters.

Embodiment 63: The apparatus of embodiment 62 in which the wavelengthdivision demultiplexer is configured to split incoming light into afirst beam and a second beam, direct the first beam to a first bandpassoptical filter that passes light having a first wavelength, and directthe second beam to a second bandpass optical filter that passes lighthaving a second wavelength.

Embodiment 64: The apparatus of embodiment 62 in which the wavelengthdivision demultiplexer is configured to convert K rows of N fibers to anN×2MK array of grating couplers, K, N, and M are positive integers, andM represents the number of wavelengths that is processed by thewavelength division demultiplexer.

Embodiment 65: The apparatus of embodiment 1 in which the fiber-opticconnector comprises a wavelength division multiplexer that includes oneor more broadband optical splitters.

Embodiment 66: The apparatus of embodiment 65 in which the wavelengthdivision multiplexer is configured to combine light having a firstwavelength from a first set of one or more grating couplers and lighthaving a second wavelength from a second set of one or more gratingcouplers into a combined optical beam.

Embodiment 67: The apparatus of embodiment 65 in which the wavelengthdivision multiplexer is configured to convert an N×2MK array of gratingcouplers into K rows of N fibers, K, N, and M are positive integers, andM represents the number of wavelengths that is processed by thewavelength division multiplexer.

Embodiment 68: The apparatus of embodiment 1 in which the fiber-opticconnector comprises an isolator that is configured to direct egresslight leaving the photonic integrated circuit in an egress path that isdifferent from an ingress path traveled by ingress light, and the egresslight is not coupled back into an optical fiber that provides theingress light.

Embodiment 69: The apparatus of embodiment 68 in which the isolatorcomprises a walk-off element and at least one non-reciprocal rotator.

Embodiment 70: An apparatus comprising:

-   -   a laser configured to provide optical power supply light;    -   a first linear-polarization-maintaining fiber optically coupled        to the laser to receive the optical power supply light;    -   a polarization beam splitter, in which the        linear-polarization-maintaining fiber is oriented at an angle        relative to the polarization beam splitter to achieve an optical        power split of the optical power supply light to generate a        first power supply light having a first polarization and a        second power supply light having a second polarization;    -   a second linear-polarization-maintaining fiber optically coupled        to a first port of the polarization beam splitter to receive the        first power supply light; and a third        linear-polarization-maintaining fiber optically coupled to a        second port of the polarization beam splitter to receive the        second power supply light.

Embodiment 71: An apparatus comprising:

-   -   a laser configured to provide linearly polarized optical power        supply light;    -   a quarter-wave plate to convert the linear polarized optical        power supply light to circular polarized optical power supply        light;    -   a circular-polarization-maintaining fiber configured to        propagate the circular polarized optical power supply light from        the quarter-wave plate;    -   a polarization beam splitter configured to split the circular        polarized optical power supply light to generate first power        supply light having a first polarization and second power supply        light having a second polarization;    -   a first linear-polarization-maintaining fiber optically coupled        to a first port of the polarization beam splitter to receive the        first power supply light; and a second        linear-polarization-maintaining fiber optically coupled to a        second port of the polarization beam splitter to receive the        second power supply light.

Embodiment 72: An apparatus comprising:

-   -   a fiber-optic connector comprising:        -   a set of fiber ports configured to be optically coupled to            one or more optical fibers having a plurality of fiber            cores;        -   a set of optical ports configured to be optically coupled to            a plurality of coupling elements of a photonic integrated            circuit; and        -   optics configured to transfer light between the set of fiber            ports and the set of optical ports;        -   wherein the optics comprise at least one of (i) one or more            polarization beam splitters, (ii) one or more            polarization-rotating elements, (iii) one or more walk-off            elements, (iv) a birefringent hole plate, (v) a wavelength            division multiplexer, (vi) a wavelength division            demultiplexer, or (vii) an isolator.

Embodiment 73: The apparatus of embodiment 72 in which the fiber-opticconnector is configured to receive a first optical power supply beamfrom the set of fiber ports, split the first optical power supply beaminto a second optical power supply beam and a third optical power supplybeam, and output the second and third optical power supply beams throughthe set of optical ports.

Embodiment 74: The apparatus of embodiment 73 in which the fiber-opticconnector comprises the fiber-optic connector of any of embodiments 39to 43.

Embodiment 75: The apparatus of any of embodiments 71 to 74 in which thebirefringent hole plate comprises the birefringent hole plate of any ofembodiments 21 to 23, 25 to 36, and 45 to 49.

Embodiment 76: The apparatus of any of embodiments 71 to 75 in which theone or more walk-off elements comprise the walk-off element of any ofembodiments 26 to 36, 45 to 49, and 69.

Embodiment 77: The apparatus of any of embodiments 71 to 76 in which thewavelength division multiplexer comprises the wavelength divisionmultiplexer of any of embodiments 44 to 52, 59 to 61, and 65 to 67.

Embodiment 78: The apparatus of any of embodiments 71 to 77 in which thewavelength division demultiplexer comprises the wavelength divisiondemultiplexer of any of embodiments 56 to 58 and 62 to 64.

Embodiment 79: The apparatus of any of embodiments 71 to 78 in which theisolator comprises the isolator of embodiment 68 or 69.

Embodiment 80: A data center comprising the apparatus of any ofembodiments 1 to 79.

Embodiment 81: A method of operating the apparatus of any of embodiments1 to 79.

Embodiment 82: A method of operating the data center of embodiment 80.

Embodiment 83: A method of assembling the apparatus of any ofembodiments 1 to 79.

Embodiment 84: A method of processing data using the apparatus of any ofembodiments 1 to 79.

Embodiment 85: A method of providing optical power using the apparatusof any of embodiments 39 to 43, 70, and 71.

The following is a second set of embodiments. The embodiment numbersbelow refer to those in the second set of embodiments.

Embodiment 1: An apparatus comprising:

-   -   a laser configured to provide linearly polarized optical power        supply light;    -   a quarter-wave plate to convert the linearly polarized optical        power supply light to circularly polarized optical power supply        light;    -   a circular-polarization-maintaining fiber configured to        propagate the circularly polarized optical power supply light        from the quarter-wave plate;    -   a polarization beam splitter configured to split the circularly        polarized optical power supply light to generate first power        supply light having a first polarization and second power supply        light having a second polarization;    -   a first linear-polarization-maintaining fiber optically coupled        to a first port of the polarization beam splitter to receive the        first power supply light; and    -   a second linear-polarization-maintaining fiber optically coupled        to a second port of the polarization beam splitter to receive        the second power supply light.

Embodiment 2: An apparatus comprising:

-   -   a first laser configured to generate first linearly polarized        light;    -   a first quarter-wave plate configured to convert the first        linearly polarized light to first circularly polarized light;    -   a first circular-polarization-maintaining fiber having a first        end optically coupled to the first quarter-wave plate;    -   a second quarter-wave plate optically coupled to a second end of        the first circular-polarization-maintaining fiber, in which the        first circular-polarization-maintaining fiber is configured to        transmit the first circularly polarized light from the first        quarter-wave plate to the second quarter-wave plate, and the        second quarter-wave plate is configured to convert the first        circularly polarized light to second linearly polarized light;        and    -   a first optical modulator configured to modulate the second        linearly polarized light.

Embodiment 3: The apparatus of embodiment 2, comprising a first photonicintegrated circuit including circuitry that is configured to generate afirst electrical signal, in which the first optical modulator is part ofthe photonic integrated circuit, and the first optical modulator isconfigured to modulate the second linearly polarized light based on thefirst electrical signal.

Embodiment 4: The apparatus of embodiment 2 or 3, comprising:

-   -   a second laser configured to generate third linearly polarized        light, in which the first quarter-wave plate is configured to        convert the third linearly polarized light to second circularly        polarized light;    -   a second circular-polarization-maintaining fiber having a first        end optically coupled to the first quarter-wave plate and a        second end optically coupled to the second quarter-wave plate,        in which the second circular-polarization-maintaining fiber is        configured to transmit the second circularly polarized light        from the first quarter-wave plate to the second quarter-wave        plate;    -   wherein the second quarter-wave plate is configured to convert        the second circularly polarized light to fourth linearly        polarized light; and a second optical modulator configured to        modulate the fourth linearly polarized light.

Embodiment 5: The apparatus of embodiment 4 in which the first laser andthe second laser are aligned such that the first linearly polarizedlight has a polarization direction that is substantially parallel to thepolarization direction of the third linearly polarized light.

Embodiment 6: The apparatus of embodiment 4 or 5, comprising asubstrate, in which the first optical modulator and the second opticalmodulator are mounted on the substrate.

Embodiment 7: The apparatus of embodiment 6 in which the secondquarter-wave plate is at least one of edge-coupled or vertically coupledto the substrate.

Embodiment 8: An apparatus comprising:

-   -   a first substrate;    -   a first laser mounted on the first substrate and configured to        generate first linearly polarized light;    -   a first quarter-wave polarization rotator mounted on the first        substrate and configured to convert the first linearly polarized        light to first circularly polarized light; a first        circular-polarization-maintaining fiber having a first end        optically coupled to the first quarter-wave polarization        rotator;    -   a second substrate;    -   a second quarter-wave polarization rotator mounted on the second        substrate and optically coupled to a second end of the first        circular-polarization-maintaining fiber, in which the first        circular-polarization-maintaining fiber is configured to        transmit the first circularly polarized light from the first        quarter-wave polarization rotator to the second quarter-wave        polarization rotator, and the second quarter-wave polarization        rotator is configured to convert the first circularly polarized        light to second linearly polarized light; and    -   a first optical modulator mounted on the second substrate and        configured to modulate the second linearly polarized light.

Embodiment 9: The apparatus of embodiment 8 in which the firstcircular-polarization-maintaining fiber is at least one of edge-coupledor vertically coupled to the second substrate.

Embodiment 10: The apparatus of embodiment 8 or 9, comprising:

-   -   a second laser mounted on the first substrate and configured to        generate third linearly polarized light;    -   a third quarter-wave polarization rotator mounted on the first        substrate and configured to convert the third linearly polarized        light to second circularly polarized light;    -   a second circular-polarization-maintaining fiber having a first        end optically coupled to the second quarter-wave polarization        rotator;    -   a fourth quarter-wave polarization rotator mounted on the second        substrate and optically coupled to a second end of the second        circular-polarization-maintaining fiber, in which the second        circular-polarization-maintaining fiber is configured to        transmit the second circularly polarized light from the third        quarter-wave polarization rotator to the fourth quarter-wave        polarization rotator, and the fourth quarter-wave polarization        rotator is configured to convert the second circularly polarized        light to fourth linearly polarized light; and    -   a second optical modulator mounted on the second substrate and        configured to modulate the fourth polarized light.

Embodiment 11: The apparatus of embodiment 10 in which the first laserand the second laser are aligned such that the first linearly polarizedlight has a polarization direction that is substantially parallel to thepolarization direction of the third linearly polarized light.

Embodiment 12: An apparatus comprising:

-   -   a first laser configured to generate first linearly polarized        light;    -   a second laser configured to generate second linearly polarized        light;    -   a first polarization beam splitter configured to combine the        first linearly polarized light and the second linearly polarized        light to generate a first linearly polarized combined light;    -   a first quarter-wave plate or quarter-wave polarization rotator        configured to convert the first linearly polarized combined        light to first circularly polarized combined light;    -   a first circular-polarization-maintaining fiber having a first        end optically coupled to the first quarter-wave plate or        quarter-wave polarization rotator;    -   a second quarter-wave plate or quarter-wave polarization rotator        optically coupled to a second end of the circular polarization        maintaining fiber, in which the first        circular-polarization-maintaining fiber is configured to        transmit the first circularly polarized combined light from the        first quarter-wave plate or quarter-wave polarization rotator to        the second quarter-wave plate or quarter-wave polarization        rotator, and the second quarter-wave plate or quarter-wave        polarization rotator is configured to convert the first        circularly polarized combined light to second linearly polarized        combined light;    -   a second polarization beam splitter configured to separate the        second linearly polarized combined light to a third linearly        polarized light and a fourth linearly polarized light;    -   a first optical modulator configured to modulate the third        linearly polarized light; and    -   a second optical modulator configured to modulate the fourth        linearly polarized light.

Embodiment 13: The apparatus of embodiment 12 in which the firstlinearly polarized light has a first polarization direction, and thesecond linearly polarized light has a second polarization direction thatis substantially orthogonal to the first polarization direction.

Embodiment 14: The apparatus of embodiment 13 in which the thirdlinearly polarized light has a third polarization direction, and thefourth linearly polarized light has a fourth polarization direction thatis substantially orthogonal to the third polarization direction.

Embodiment 15: The apparatus of embodiment 13 or 14 in which the firstcircularly polarized combined light has a right-handed circularlypolarized component and a left-handed circularly polarized component.

Embodiment 16: An apparatus comprising:

-   -   a photon source comprising a first laser source and a second        laser source, in which the photon source is configured to        generate first circularly polarized combined light based on        light generated by the first laser source and the second laser        source, the first circularly polarized combined light has a        right-handed circularly polarized component and a left-handed        circularly polarized component;    -   a first circular-polarization-maintaining fiber configured to        receive the first circularly polarized combined light from the        photon source; and    -   a modulator module comprising a first modulator and a second        modulator, in which the modulator module is configured to        convert the first circularly polarized combined light to third        linearly polarized light and fourth linearly polarized light,        the first modulator is configured to modulate the third linearly        polarized light, and the second modulator is configured to        modulate the fourth linearly polarized light.

Embodiment 17: The apparatus of embodiment 16 in which the photon sourcecomprises a first polarization beam splitter configured to combine lightgenerated by the first laser source and light generated by the secondlaser source.

Embodiment 18: The apparatus of embodiment 17 in which the first lasersource is configured to generate first linearly polarized light, and thesecond laser source is configured to generate second linearly polarizedlight having a polarization direction that is substantially orthogonalto the polarization direction of the first linearly polarized light.

Embodiment 19: The apparatus of embodiment 18 in which the second lasersource comprises a second laser and a polarization rotator, the secondlaser is configured to generate linearly polarized light having apolarization direction that is substantially parallel to thepolarization direction of the first linearly polarized light, and

-   -   the polarization rotator is configured to rotate the        polarization direction of the light from the second laser to        cause the second linearly polarized light to have the        polarization direction that is substantially orthogonal to the        polarization direction of the first linearly polarized light.

Embodiment 20: The apparatus of any of embodiments 17 to 19 in which thephoton source comprises a first quarter-wave plate configured to receivelight from the polarization beam splitter,

-   -   the first laser source is configured to generate first linearly        polarized light, the second laser source is configured to        generate second linearly polarized light having a polarization        direction substantially orthogonal to the polarization direction        of the first linearly polarized light,    -   the first polarization beam splitter is configured to combine        the first linearly polarized light and the second linearly        polarized light to generate first linearly polarized combined        light, and    -   the first quarter-wave plate is configured to convert the first        linearly polarized combined light to the first circularly        polarized combined light.

Embodiment 21: The apparatus of any of embodiments 17 to 19 in which thephoton source comprises a first quarter-wave plate configured to receivelight from the first laser source and the second laser source,

-   -   the first laser source is configured to generate first linearly        polarized light, the second laser source is configured to        generate second linearly polarized light having a polarization        direction substantially orthogonal to the polarization direction        of the first linearly polarized light,    -   the first quarter-wave plate is configured to convert the first        linearly polarized light to first circularly polarized light,        and convert the second linearly polarized light to second        circularly polarized light, and    -   the first polarization beam splitter is configured to combine        the first circularly polarized light and the second circularly        polarized light to generate the first circularly polarized        combined light.

Embodiment 22: The apparatus of any of embodiments 16 to 21 in which themodulator module comprises a second polarization beam splitterconfigured to separate the first circularly polarized combined light orlight derived from the first circularly polarized combined light to afirst light component that is provided to the first modulator and asecond light component that is provided to the second modulator.

Embodiment 23: The apparatus of embodiment 22 in which the modulatormodule comprises a quarter-wave plate configured to receive the firstcircularly polarized combined light and generate second linearlypolarized combined light,

-   -   the second polarization beam splitter is configured to separate        the second linearly polarized combined light to the third        linearly polarized light and the fourth linearly polarized        light.

Embodiment 24: The apparatus of embodiment 22 in which the modulatormodule comprises a quarter-wave plate configured to receive light fromthe second polarization beam splitter,

-   -   the second polarization beam splitter is configured to separate        the first circularly polarized combined light to a first        circularly polarized component and a second circularly polarized        component,    -   the quarter-wave plate is configured to convert the first        circularly polarized component to the third linearly polarized        light, and convert the second circularly polarized component to        the fourth linearly polarized light.

Embodiment 25: The apparatus of any of embodiments 22 to 24 in which themodulator module comprises a polarization rotator configured to rotatethe polarization direction of the light that is provided to one of themodulators.

Embodiment 26: A method comprising:

-   -   at a first light source, generating first circularly polarized        light;    -   transmitting the first circularly polarized light through a        first circular-polarization-maintaining fiber from the first        light source to a second location;    -   at the second location, converting the first circularly        polarized light to second linearly polarized light; and    -   modulating the second linearly polarized light.

Embodiment 27: The method of embodiment 26 in which generating the firstcircularly polarized light comprises generating first linearly polarizedlight, and converting the first linearly polarized light to the firstcircularly polarized light.

Embodiment 28: The method of embodiment 26 in which generating the firstcircularly polarized light comprises:

-   -   generating first linearly polarized light,    -   generating third linearly polarized light,    -   combining the first linearly polarized light and the third        linearly polarized light to generate first linearly polarized        combined light, and    -   converting the first linearly polarized combined light to the        first circularly polarized light, in which the first circularly        polarized light includes a first circularly polarized component        and a second circularly polarized component.

Embodiment 29: The method of embodiment 26 in which generating the firstcircularly polarized light comprises:

-   -   generating first linearly polarized light,    -   generating third linearly polarized light,    -   converting the first linearly polarized light to second        circularly polarized light,    -   converting the third linearly polarized light to third        circularly polarized light, and    -   combining the second circularly polarized light and the third        circularly polarized light to generate the first circularly        polarized combined light.

Embodiment 30: The method of embodiment 28 or 29 in which converting thefirst circularly polarized light to second linearly polarized lightcomprises converting the first circularly polarized light to thirdlinearly polarized light, and separating the third linearly polarizedlight to fourth linearly polarized light and fifth linearly polarizedlight,

-   -   wherein modulating the second linearly polarized light comprises        modulating the fourth linearly polarized light and modulating        the fifth linearly polarized light.

Embodiment 31: The method of embodiment 28 or 29 in which converting thefirst circularly polarized light to second linearly polarized lightcomprises separating the first circularly polarized light to a firstcircularly polarized component and a second circularly polarizedcomponent, converting the first circularly polarized component to thirdlinearly polarized light, converting the second circularly polarizedcomponent to fourth linearly polarized light,

-   -   wherein modulating the second linearly polarized light comprises        modulating the third linearly polarized light and modulating the        fourth linearly polarized light.

Embodiment 32: A method comprising:

-   -   using a first single quarter-wave plate to convert a first        plurality of linearly polarized light to a plurality of        circularly polarized light;    -   transmitting the plurality of circularly polarized light through        a plurality of circular-polarization-maintaining fibers;    -   converting the circularly polarized light received from the        plurality of circular-polarization-maintaining fibers to a        second plurality of linearly polarized light; and    -   modulating the second plurality of linearly polarized light.

Embodiment 33: The method of embodiment 32 in which converting thecircularly polarized light received from the plurality ofcircular-polarization-maintaining fibers to the second plurality oflinearly polarized light comprises using a second single quarter-waveplate to convert the circularly polarized light received from theplurality of circular-polarization-maintaining fibers to the secondplurality of linearly polarized light.

Embodiment 34: A method comprising:

-   -   at a first photonic integrated circuit, generating a first        plurality of linearly polarized light, and converting the first        plurality of linearly polarized light to a plurality of        circularly polarized light;    -   transmitting the plurality of circularly polarized light through        a plurality of circular-polarization-maintaining fibers from the        first photonic integrated circuit to a second location;    -   at the second location, converting the plurality of circularly        polarized light to a second plurality of linearly polarized        light; and    -   modulating the second plurality of linearly polarized light.

Embodiment 35: The method of embodiment 34 in which converting the firstplurality of linearly polarized light to the plurality of circularlypolarized light comprises using a plurality of polarization convertersto convert the first plurality of linearly polarized light to theplurality of circularly polarized light.

Embodiment 36: The method of embodiment 34 or 35 in which converting theplurality of circularly polarized light to the second plurality oflinearly polarized light comprises using a plurality of polarizationconverters to convert the plurality of circularly polarized light to thesecond plurality of linearly polarized light.

Embodiment 37: An apparatus comprising:

-   -   a light source configured to generate first linearly polarized        light;    -   a first quarter-wave plate configured to convert the first        linearly polarized light to first circularly polarized light;    -   a first circular-polarization-maintaining fiber having a first        end optically coupled to the first quarter-wave plate;    -   a second quarter-wave plate optically coupled to a second end of        the first circular-polarization-maintaining fiber, in which the        first circular-polarization-maintaining fiber is configured to        transmit the first circularly polarized light from the first        quarter-wave plate to the second quarter-wave plate, and the        second quarter-wave plate is configured to convert the first        circularly polarized light to second linearly polarized light;        and    -   a first optical device that accepts the second linearly        polarized light.

Embodiment 38: The apparatus of embodiment 37 in which the first opticaldevice comprise at least one of a lithium niobate optical modulator, avertical grating coupler on a photonic integrated circuit, or amodulator integrated on a photonic integrated circuit.

Embodiment 39: The apparatus of embodiment 37 in which the light sourcecomprises a local oscillator that is configured to generate a sequenceof optical pulses, and the first optical device comprises a coherentoptical receiver.

Embodiment 40: The apparatus of embodiment 37 in which the light sourcecomprises a single-polarization optical transmitter and the firstoptical device comprises a single-polarization optical receiver.

Embodiment 41: The apparatus of embodiment 37, comprising a firstphotonic integrated circuit including circuitry that is configured togenerate a first electrical signal, in which the first optical device ispart of the photonic integrated circuit, and the first optical device isconfigured to process the second linearly polarized light based on thefirst electrical signal.

Embodiment 42: The apparatus of any of embodiments 37 to 41, comprising:

-   -   a second light source configured to generate third linearly        polarized light, in which the first quarter-wave plate is        configured to convert the third linearly polarized light to        second circularly polarized light;    -   a second circular-polarization-maintaining fiber having a first        end optically coupled to the first quarter-wave plate and a        second end optically coupled to the second quarter-wave plate,        in which the second circular-polarization-maintaining fiber is        configured to transmit the second circularly polarized light        from the first quarter-wave plate to the second quarter-wave        plate;    -   wherein the second quarter-wave plate is configured to convert        the second circularly polarized light to fourth linearly        polarized light; and    -   a second optical device that accepts the fourth linearly        polarized light.

Embodiment 43: The apparatus of embodiment 42 in which the first lightsource and the second light source are aligned such that the firstlinearly polarized light has a polarization direction that issubstantially parallel to the polarization direction of the thirdlinearly polarized light.

Embodiment 44: The apparatus of embodiment 42 or 43, comprising asubstrate, in which the first optical device and the second opticaldevice are mounted on the substrate.

Embodiment 45: The apparatus of embodiment 44 in which the secondquarter-wave plate is at least one of edge-coupled or vertically coupledto the substrate.

Embodiment 46: An apparatus comprising:

-   -   a first substrate;    -   a first light source mounted on the first substrate and        configured to generate first linearly polarized light;    -   a first quarter-wave polarization rotator mounted on the first        substrate and configured to convert the first linearly polarized        light to first circularly polarized light;    -   a first circular-polarization-maintaining fiber having a first        end optically coupled to the first quarter-wave polarization        rotator;    -   a second substrate;    -   a second quarter-wave polarization rotator mounted on the second        substrate and optically coupled to a second end of the first        circular-polarization-maintaining fiber, in which the first        circular-polarization-maintaining fiber is configured to        transmit the first circularly polarized light from the first        quarter-wave polarization rotator to the second quarter-wave        polarization rotator, and the second quarter-wave polarization        rotator is configured to convert the first circularly polarized        light to second linearly polarized light; and    -   a first optical device mounted on the second substrate and        configured to modulate the second linearly polarized light.

Embodiment 47: The apparatus of embodiment 46 in which the firstcircular-polarization-maintaining fiber is at least one of edge-coupledor vertically coupled to the second substrate.

Embodiment 48: The apparatus of embodiment 46 or 47, comprising:

-   -   a second light source mounted on the first substrate and        configured to generate third linearly polarized light;    -   a third quarter-wave polarization rotator mounted on the first        substrate and configured to convert the third linearly polarized        light to second circularly polarized light;    -   a second circular-polarization-maintaining fiber having a first        end optically coupled to the second quarter-wave polarization        rotator;    -   a fourth quarter-wave polarization rotator mounted on the second        substrate and optically coupled to a second end of the second        circular-polarization-maintaining fiber, in which the second        circular-polarization-maintaining fiber is configured to        transmit the second circularly polarized light from the third        quarter-wave polarization rotator to the fourth quarter-wave        polarization rotator, and the fourth quarter-wave polarization        rotator is configured to convert the second circularly polarized        light to fourth linearly polarized light; and    -   a second optical modulator mounted on the second substrate and        configured to modulate the fourth polarized light.

Embodiment 49: The apparatus of embodiment 48 in which the first lightsource and the second light source are aligned such that the firstlinearly polarized light has a polarization direction that issubstantially parallel to the polarization direction of the thirdlinearly polarized light.

Embodiment 50: An apparatus comprising:

-   -   a first light source configured to generate first linearly        polarized light;    -   a second light source configured to generate second linearly        polarized light;    -   a first polarization beam splitter configured to combine the        first linearly polarized light and the second linearly polarized        light to generate a first linearly polarized combined light;    -   a first quarter-wave plate or quarter-wave polarization rotator        configured to convert the first linearly polarized combined        light to first circularly polarized combined light;    -   a first circular-polarization-maintaining fiber having a first        end optically coupled to the first quarter-wave plate or        quarter-wave polarization rotator;    -   a second quarter-wave plate or quarter-wave polarization rotator        optically coupled to a second end of the circular polarization        maintaining fiber, in which the first        circular-polarization-maintaining fiber is configured to        transmit the first circularly polarized combined light from the        first quarter-wave plate or quarter-wave polarization rotator to        the second quarter-wave plate or quarter-wave polarization        rotator, and the second quarter-wave plate or quarter-wave        polarization rotator is configured to convert the first        circularly polarized combined light to second linearly polarized        combined light;    -   a second polarization beam splitter configured to separate the        second linearly polarized combined light to a third linearly        polarized light and a fourth linearly polarized light;    -   a first optical device configured to process the third linearly        polarized light; and    -   a second optical device configured to process the fourth        linearly polarized light.

Embodiment 51: The apparatus of embodiment 50 in which the firstlinearly polarized light has a first polarization direction, and thesecond linearly polarized light has a second polarization direction thatis substantially orthogonal to the first polarization direction.

Embodiment 52: The apparatus of embodiment 51 in which the thirdlinearly polarized light has a third polarization direction, and thefourth linearly polarized light has a fourth polarization direction thatis substantially orthogonal to the third polarization direction.

Embodiment 53: The apparatus of embodiment 51 or 52 in which the firstcircularly polarized combined light has a right-handed circularlypolarized component and a left-handed circularly polarized component.

Embodiment 54: An apparatus comprising:

-   -   a photon source comprising a first light source and a second        light source, in which the photon source is configured to        generate first circularly polarized combined light based on        light generated by the first light source and the second light        source, the first circularly polarized combined light has a        right-handed circularly polarized component and a left-handed        circularly polarized component;    -   a first circular-polarization-maintaining fiber configured to        receive the first circularly polarized combined light from the        photon source; and    -   an optical module comprising a first optical device and a second        optical device, in which the optical module is configured to        convert the first circularly polarized combined light to third        linearly polarized light and fourth linearly polarized light,        the first optical device is configured to process the third        linearly polarized light, and the second optical device is        configured to process the fourth linearly polarized light.

Embodiment 55: The apparatus of embodiment 54 in which the photon sourcecomprises a first polarization beam splitter configured to combine lightgenerated by the first light source and light generated by the secondlight source.

Embodiment 56: The apparatus of embodiment 55 in which the first lightsource is configured to generate first linearly polarized light, and

-   -   the second light source is configured to generate second        linearly polarized light having a polarization direction that is        substantially orthogonal to the polarization direction of the        first linearly polarized light.

Embodiment 57: The apparatus of embodiment 56 in which the second lightsource comprises a second light generating device and a polarizationrotator, the second light generating device is configured to generatelinearly polarized light having a polarization direction that issubstantially parallel to the polarization direction of the firstlinearly polarized light, and

-   -   the polarization rotator is configured to rotate the        polarization direction of the light from the second light        generating device to cause the second linearly polarized light        to have the polarization direction that is substantially        orthogonal to the polarization direction of the first linearly        polarized light.

Embodiment 58: The apparatus of any of embodiments 55 to 57 in which thephoton source comprises a first quarter-wave plate configured to receivelight from the polarization beam splitter,

-   -   the first light source is configured to generate first linearly        polarized light, the second light source is configured to        generate second linearly polarized light having a polarization        direction substantially orthogonal to the polarization direction        of the first linearly polarized light,    -   the first polarization beam splitter is configured to combine        the first linearly polarized light and the second linearly        polarized light to generate first linearly polarized combined        light, and    -   the first quarter-wave plate is configured to convert the first        linearly polarized combined light to the first circularly        polarized combined light.

Embodiment 59: The apparatus of any of embodiments 55 to 57 in which thephoton source comprises a first quarter-wave plate configured to receivelight from the first light source and the second light source,

-   -   the first light source is configured to generate first linearly        polarized light, the second light source is configured to        generate second linearly polarized light having a polarization        direction substantially orthogonal to the polarization direction        of the first linearly polarized light,    -   the first quarter-wave plate is configured to convert the first        linearly polarized light to first circularly polarized light,        and convert the second linearly polarized light to second        circularly polarized light, and    -   the first polarization beam splitter is configured to combine        the first circularly polarized light and the second circularly        polarized light to generate the first circularly polarized        combined light.

Embodiment 60: The apparatus of any of embodiments 54 to 59 in which theoptical module comprises a second polarization beam splitter configuredto separate the first circularly polarized combined light or lightderived from the first circularly polarized combined light to a firstlight component that is provided to the first modulator and a secondlight component that is provided to the second optical device.

Embodiment 61: The apparatus of embodiment 60 in which the opticalmodule comprises a quarter-wave plate configured to receive the firstcircularly polarized combined light and generate second linearlypolarized combined light,

-   -   the second polarization beam splitter is configured to separate        the second linearly polarized combined light to the third        linearly polarized light and the fourth linearly polarized        light.

Embodiment 62: The apparatus of embodiment 60 in which the opticalmodule comprises a quarter-wave plate configured to receive light fromthe second polarization beam splitter,

-   -   the second polarization beam splitter is configured to separate        the first circularly polarized combined light to a first        circularly polarized component and a second circularly polarized        component,    -   the quarter-wave plate is configured to convert the first        circularly polarized component to the third linearly polarized        light, and convert the second circularly polarized component to        the fourth linearly polarized light.

Embodiment 63: The apparatus of any of embodiments 60 to 62 in which theoptical module comprises a polarization rotator configured to rotate thepolarization direction of the light that is provided to one of theoptical devices.

Embodiment 64: A method comprising:

-   -   at a first light source, generating first circularly polarized        light;    -   transmitting the first circularly polarized light through a        first circular-polarization-maintaining fiber from the first        light source to a second location;    -   at the second location, converting the first circularly        polarized light to second linearly polarized light; and    -   processing the second linearly polarized light.

Embodiment 65: The method of embodiment 64 in which generating the firstcircularly polarized light comprises generating first linearly polarizedlight, and converting the first linearly polarized light to the firstcircularly polarized light.

Embodiment 66: The method of embodiment 64 in which generating the firstcircularly polarized light comprises:

-   -   generating first linearly polarized light,    -   generating third linearly polarized light,    -   combining the first linearly polarized light and the third        linearly polarized light to generate first linearly polarized        combined light, and    -   converting the first linearly polarized combined light to the        first circularly polarized light, in which the first circularly        polarized light includes a first circularly polarized component        and a second circularly polarized component.

Embodiment 67: The method of embodiment 64 in which generating the firstcircularly polarized light comprises:

-   -   generating first linearly polarized light,    -   generating third linearly polarized light,    -   converting the first linearly polarized light to second        circularly polarized light,    -   converting the third linearly polarized light to third        circularly polarized light, and    -   combining the second circularly polarized light and the third        circularly polarized light to generate the first circularly        polarized combined light.

Embodiment 68: The method of embodiment 66 or 67 in which converting thefirst circularly polarized light to second linearly polarized lightcomprises converting the first circularly polarized light to thirdlinearly polarized light, and separating the third linearly polarizedlight to fourth linearly polarized light and fifth linearly polarizedlight,

-   -   wherein processing the second linearly polarized light comprises        processing the fourth linearly polarized light and processing        the fifth linearly polarized light.

Embodiment 69: The method of embodiment 66 or 67 in which converting thefirst circularly polarized light to second linearly polarized lightcomprises separating the first circularly polarized light to a firstcircularly polarized component and a second circularly polarizedcomponent, converting the first circularly polarized component to thirdlinearly polarized light, converting the second circularly polarizedcomponent to fourth linearly polarized light,

-   -   wherein processing the second linearly polarized light comprises        processing the third linearly polarized light and processing the        fourth linearly polarized light.

Embodiment 70: A method comprising:

-   -   using a first single quarter-wave plate to convert a first        plurality of linearly polarized light to a plurality of        circularly polarized light;    -   transmitting the plurality of circularly polarized light through        a plurality of circular-polarization-maintaining fibers;    -   converting the circularly polarized light received from the        plurality of circular-polarization-maintaining fibers to a        second plurality of linearly polarized light; and    -   processing the second plurality of linearly polarized light.

Embodiment 71: The method of embodiment 70 in which converting thecircularly polarized light received from the plurality ofcircular-polarization-maintaining fibers to the second plurality oflinearly polarized light comprises using a second single quarter-waveplate to convert the circularly polarized light received from theplurality of circular-polarization-maintaining fibers to the secondplurality of linearly polarized light.

Embodiment 72: A method comprising:

-   -   at a first photonic integrated circuit, generating a first        plurality of linearly polarized light, and converting the first        plurality of linearly polarized light to a plurality of        circularly polarized light;    -   transmitting the plurality of circularly polarized light through        a plurality of circular-polarization-maintaining fibers from the        first photonic integrated circuit to a second location;    -   at the second location, converting the plurality of circularly        polarized light to a second plurality of linearly polarized        light; and    -   processing the second plurality of linearly polarized light.

Embodiment 73: The method of embodiment 72 in which converting the firstplurality of linearly polarized light to the plurality of circularlypolarized light comprises using a plurality of polarization convertersto convert the first plurality of linearly polarized light to theplurality of circularly polarized light.

Embodiment 74: The method of embodiment 72 or 73 in which converting theplurality of circularly polarized light to the second plurality oflinearly polarized light comprises using a plurality of polarizationconverters to convert the plurality of circularly polarized light to thesecond plurality of linearly polarized light.

Embodiment 75: A data center comprising the apparatus of any ofembodiments 1 to 25 and 37 to 63.

Embodiment 76: A method of operating the apparatus of any of embodiments1 to 25 and 37 to 63.

Embodiment 77: A method of operating the data center of embodiment 75.

Embodiment 78: A method of assembly the apparatus of any of embodiments1 to 25 and 37 to 63.

Embodiment 79: A method of processing data using the apparatus of any ofembodiments 1 to 25 and 37 to 63.

The following is a third set of embodiments. The embodiment numbersbelow refer to those in the third set of embodiments.

Embodiment 1: An apparatus comprising:

-   -   a fiber-optic connector configured to optically couple a        plurality of optical fibers to a plurality of vertical coupling        elements on a photonic integrated circuit, in which the        fiber-optic connector comprises a plurality of circularly        asymmetric optical lenses configured to direct light toward the        vertical coupling elements at one or more angles of incidence        relative to a direction perpendicular to a main surface of the        photonic integrated circuit.

Embodiment 2: An apparatus comprising:

-   -   a fiber-optic connector configured to optically couple a        plurality of optical fibers to a plurality of vertical coupling        elements on a photonic integrated circuit, in which the        fiber-optic connector comprises a plurality of circularly        asymmetric optical lenses configured to direct light from the        optical fibers toward the vertical coupling elements,    -   wherein each of at least some of the circularly asymmetric        optical lenses is configured to direct a light beam towards the        corresponding vertical coupling element at an angle of incidence        relative to a direction perpendicular to a main surface of the        photonic integrated circuit, and each of at least some of the        circularly asymmetric optical lenses is asymmetric with respect        to an optical axis that is perpendicular to the main surface of        the photonic integrated circuit.

Embodiment 3: The apparatus of embodiment 1 or 2 in which the pluralityof circularly asymmetric optical lenses are configured to direct lighttoward the vertical coupling elements at one or more angles of incidencein a range from 1° to 30° relative to the direction perpendicular to themain surface of the photonic integrated circuit.

Embodiment 4: The apparatus of any of embodiments 1 to 3 in which theplurality of optical fibers are arranged in a two-dimensional array.

Embodiment 5: The apparatus of embodiment 4 in which the two-dimensionalarray comprises at least 2 rows and at least 8 columns.

Embodiment 6: The apparatus of embodiment 4 or 5 in which the spacingbetween two adjacent rows in the two-dimensional array is identical tothe spacing between two adjacent columns in the two-dimensional array.

Embodiment 7: The apparatus of any of embodiments 1 to 6 in which thefiber-optic connector comprises first optical elements configured toprocess light from the optical fibers to form light beams that aredirected to the circularly asymmetric optical lenses.

Embodiment 8: The apparatus of embodiment 7 in which the first opticalelements are configured to collimate light from the optical fibers toform collimated light beams that are directed to the circularlyasymmetric optical lenses.

Embodiment 9: The apparatus of embodiment 7 or 8 in which each of atleast some of the circularly asymmetric optical lenses has a surfaceprofile that is configured to focus the light beam to a first locationon the vertical coupling element, the circularly asymmetric optical lenshas an optical axis that passes the first location,

-   -   wherein the first optical element is positioned and oriented        relative to the circularly asymmetric optical lens such that the        light beam has a first axis that is parallel to, and offset at a        first distance from, the optical axis of the circularly        asymmetric optical lens.

Embodiment 10: The apparatus of embodiment 9 in which at least twocircularly asymmetric optical lenses are spaced apart at a seconddistance in a range from 1.5 to 4.5 times the first distance between thefirst axis and the optical axis, the second distance represents thedistance between the optical axes of the lenses, the first and seconddistances being measured along a plane parallel to the main surface ofthe photonic integrated circuit.

Embodiment 11: The apparatus of embodiment 10 in which the seconddistance is in a range from 2 to 3.5 times the first distance.

Embodiment 12: The apparatus of embodiment 11 in which the seconddistance is in a range from 2 to 3 times the first distance.

Embodiment 13: The apparatus of embodiment 9 in which the plurality ofcircularly asymmetric optical lenses comprise an array of circularlyasymmetric optical lenses, and each of at least some of the circularlyasymmetric optical lenses is spaced apart from a neighboring circularlyasymmetric optical lens at a second distance in a range from 1.5 to 4.5times the first distance between the first axis and the optical axis ofthe circularly asymmetric optical lens.

Embodiment 14: The apparatus of embodiment 13 in which the seconddistance is in a range from 2 to 3.5 times the first distance.

Embodiment 15: The apparatus of embodiment 14 in which the seconddistance is in a range from 2 to 3 times the first distance.

Embodiment 16: The apparatus of any of embodiments 7 to 15 in which thefirst axis and the optical axis are perpendicular to the main surface ofthe photonic integrated circuit.

Embodiment 17: The apparatus of any of embodiments 9 to 16 in which eachof at least some of the circularly asymmetric optical lenses and thecorresponding first optical element are positioned relative to thevertical coupling element such that the first distance between the firstaxis and the optical axis is in a range from 10% to 150% of the fullwidth at half maximum of the light beam received at the circularlyasymmetric optical lens.

Embodiment 18: The apparatus of embodiment 17 in which each of at leastsome of the circularly asymmetric optical lenses and the correspondingfirst optical element are positioned relative to the vertical couplingelement such that the first distance between the first axis and theoptical axis is in a range from 20% to 80% of the full width at halfmaximum of the light beam received at the circularly asymmetric opticallens.

Embodiment 19: The apparatus of any of embodiments 7 to 18 in which eachof at least some of the circularly asymmetric optical lenses ispositioned relative to the corresponding first optical element such thatthe portion of the light beam received at the circularly asymmetricoptical lens having an intensity greater than half maximum is entirelyoffset from the optical axis of the circularly asymmetric optical lens.

Embodiment 20: The apparatus of any of embodiments 1 to 19 in which eachof at least some of the circularly asymmetric optical lenses comprises atruncated version of a rotationally symmetric optical lens, the opticalaxis of the circularly asymmetric optical lens overlaps the optical axisof the rotationally symmetric optical lens, and the circularlyasymmetric optical lens is asymmetric with respect to the optical axis.

Embodiment 21: The apparatus of embodiment 20 in which the circularlyasymmetric optical lens has a dimension that is less than 1.5 times theradius of the rotationally symmetric optical lens, the dimension of thecircularly asymmetric optical lens and the radius of the rotationallysymmetric optical lens are measured along a plane parallel to the mainsurface of the photonic integrated circuit.

Embodiment 22: The apparatus of embodiment 21 in which the circularlyasymmetric optical lens has a dimension that is less than 1.2 times theradius of the rotationally symmetric optical lens.

Embodiment 23: The apparatus of any of embodiments 20 to 22 in whicheach of at least some of the circularly asymmetric optical lenses has afootprint that is less than 50% of a footprint of the correspondingrotationally symmetric optical lens.

Embodiment 24: The apparatus of any of embodiments 1 to 23 in which eachof at least some of the circularly asymmetric optical lenses has adimension that is less than 1.5 times the diameter of the light beamreceived at the circularly asymmetric optical lens, and the diameter ofthe light beam is the full width at half maximum of the light beam.

Embodiment 25: The apparatus of embodiment 24 in which each of at leastsome of the circularly asymmetric optical lenses has a footprint havingan area that is less than 2.25 times the area of the cross section ofthe light beam received at the circularly asymmetric optical lens, andthe area of the cross section of the light beam is calculated based onthe full width at half maximum of the light beam.

Embodiment 26: The apparatus of embodiment 24 or 25 in which each of atleast some of the circularly asymmetric optical lenses is configured toreceive the entire portion of the light beam that has an intensity athalf maximum or more.

Embodiment 27: The apparatus of any of embodiments 7 to 26 in which thefirst optical elements are configured to collimate light from opticalfibers having end facets that are polished at an angle in a range from 1to 30 degrees relative to a plane that is perpendicular to the opticalaxes of the optical fibers.

Embodiment 28: The apparatus of embodiment 27 in which the first opticalelements are configured to collimate light from optical fibers havingend facets that are polished at an angle in a range from 4 to 15 degreesrelative to the plane that is perpendicular to the optical axes of theoptical fibers.

Embodiment 29: The apparatus of embodiment 28 in which the first opticalelements are configured to collimate light from optical fibers havingend facets that are polished at an angle in a range from 6 to 10 degreesrelative to the plane that is perpendicular to the optical axes of theoptical fibers.

Embodiment 30: The apparatus of any of embodiments 27 to 29 in which thefirst optical elements comprises a second plurality of circularlyasymmetric optical lenses configured to optically couple the opticalfibers to the first plurality of circularly asymmetric optical lenses.

Embodiment 31: The apparatus of embodiment 30 in which the secondplurality of circularly asymmetric optical lenses have surface profilesthat are substantially similar to the first plurality of circularlyasymmetric optical lenses.

Embodiment 32: The apparatus of any of embodiments 1 to 31 in which theplurality of circularly asymmetric optical lenses are configured todirect light toward, or receive light from, the vertical couplingelements at one or more angles of incidence in a range from 4° to 15°relative to the direction perpendicular to the main surface of thephotonic integrated circuit.

Embodiment 33: The apparatus of embodiment 32 in which the plurality ofcircularly asymmetric optical lenses are configured to direct lighttoward, or receive light from, the vertical coupling elements at one ormore angles of incidence in a range from 5° to 12° relative to thedirection perpendicular to the main surface of the photonic integratedcircuit.

Embodiment 34: The apparatus of embodiment 33 in which the plurality ofcircularly asymmetric optical lenses are configured to direct lighttoward, or receive light from, the vertical coupling elements at one ormore angles of incidence in a range from 6° to 10° relative to thedirection perpendicular to the main surface of the photonic integratedcircuit.

Embodiment 35: The apparatus of embodiment 33 in which the plurality ofcircularly asymmetric optical lenses are configured to direct lighttoward, or receive light from, the vertical coupling elements at one ormore offset angles in a range from 7° to 9° relative to the directionperpendicular to the main surface of the photonic integrated circuit.

Embodiment 36: The apparatus of any of embodiments 1 to 35 in which eachof at least some of the circularly asymmetric optical lenses has acircular or oval circumference.

Embodiment 37: The apparatus of any of embodiments 1 to 35 in which eachof at least some of the circularly asymmetric optical lenses has apolygonal circumference.

Embodiment 38: The apparatus of any of embodiments 1 to 35 in which atleast some of the circularly asymmetric optical lenses have a sameshape.

Embodiment 39: The apparatus of any of embodiments 1 to 38 in which theplurality of circularly asymmetric optical lenses comprise an array ofrows and columns of circularly asymmetric optical lenses.

Embodiment 40: The apparatus of any of embodiments 1 to 39, comprisingthe photonic integrated circuit.

Embodiment 41: The apparatus of any of embodiments 1 to 40, comprising afirst connector element configured to be mechanically and opticallycoupled to a second connector element that is optically coupled to theplurality of optical fibers.

Embodiment 42: The apparatus of any of embodiments 1 to 41 in which thevertical coupling elements comprise vertical grating couplers.

Embodiment 43: The apparatus of any of embodiments 1 to 42 in which theplurality of circularly asymmetric optical lenses comprise siliconlenses.

Embodiment 44: The apparatus of any of embodiments 40 to 43 in which thephotonic integrated circuit comprises optical waveguides that arecoupled to the vertical coupling elements.

Embodiment 45: The apparatus of any of embodiments 1 to 44 in which thefiber-optic connector comprises one or more walk-off elements configuredto receive input optical beams from one or more of the fiber cores, andseparate each of at least some of the input optical beams into a firstoptical beam component having a first polarization and a second opticalbeam component having a second polarization, and

-   -   a birefringent plate having holes, in which the birefringent        plate is positioned relative to the one or more walk-off        elements such that each of at least some of the holes is aligned        with a corresponding first optical beam component, wherein the        birefringent plate rotates a polarization of each of at least        some of the of the second optical beam components to cause the        second optical beam component to have a same polarization as the        corresponding first optical beam component.

Embodiment 46: The apparatus of embodiment 45 in which the plurality ofcircularly asymmetric optical lenses comprise a plurality of pairs ofcircularly asymmetric optical lenses, each of at least some of the pairsof circularly asymmetric optical lenses are configured to couplecorresponding first and second optical beam components to a pair ofvertical coupling elements.

Embodiment 47: The apparatus of embodiment 45 or 46 in which the holescomprise at least one of circular holes, square holes, rectangularholes, or strip holes.

Embodiment 48: The apparatus of any of embodiments 1 to 47 in which adistance between two adjacent optical fibers is in a range from 225 μmto 275 μm, and a distance between two adjacent circularly asymmetricoptical lenses is in a range from 100√{square root over (2)} μm to150√{square root over (2)} μm.

Embodiment 49: A data center comprising the apparatus of any ofembodiments 1 to 48.

Embodiment 50: A method of operating the apparatus of any of embodiments1 to 48.

Embodiment 51: A method of operating the data center of embodiment 49.

Embodiment 52: A method of assembly the apparatus of any of embodiments1 to 48.

Embodiment 53: A method of processing data using the apparatus of any ofembodiments 1 to 48.

Embodiment 54: An apparatus comprising:

-   -   a fiber-optic connector configured to optically couple a        plurality of optical fibers to a plurality of vertical coupling        elements on a photonic integrated circuit, in which the        fiber-optic connector comprises a plurality of free-form        off-axis lenses configured to direct light toward the vertical        coupling elements at one or more angles of incidence relative to        a direction perpendicular to a main surface of the photonic        integrated circuit.

Embodiment 55: The apparatus of embodiment 54 in which the plurality offree-form off-axis lenses are configured to direct light toward thevertical coupling elements at one or more angles of incidence in a rangefrom 1° to 30° relative to the direction perpendicular to the mainsurface of the photonic integrated circuit.

Embodiment 56: The apparatus of embodiment 55 in which the plurality ofoptical fibers are arranged in a two-dimensional array.

Embodiment 57: The apparatus of embodiment 56 in which thetwo-dimensional array comprises at least 2 rows and at least 8 columns.

Embodiment 58: The apparatus of embodiment 57 in which the spacingbetween two adjacent rows in the two-dimensional array is identical tothe spacing between two adjacent columns in the two-dimensional array.

Embodiment 59: The apparatus of any of embodiments 54 to 58 in which thefiber-optic connector comprises first optical elements configured toprocess light from the optical fibers to form light beams that aredirected to the free-form off-axis lenses.

Embodiment 60: The apparatus of embodiment 59 in which the first opticalelements are configured to collimate light from the optical fibers toform collimated light beams that are directed to the free-form off-axislenses.

Embodiment 61: The apparatus of embodiment 59 or 60 in which each of atleast some of the free-form off-axis lenses has a surface profile thatis configured to focus the light beam to a first location on thevertical coupling element, the free-form off-axis lens has an opticalaxis that passes the first location,

-   -   wherein the first optical element is positioned and oriented        relative to the free-form off-axis lens such that the light beam        has a first axis that is parallel to, and offset at a first        distance from, the optical axis of the free-form off-axis lens.

Embodiment 62: An apparatus comprising:

-   -   a fiber-optic connector configured to optically couple a        plurality of optical fibers to a plurality of vertical coupling        elements on a photonic integrated circuit, wherein the        fiber-optic connector comprises:        -   a plurality of first lenses configured to collimate light            received from the optical fibers to generate collimated            light beams, each of at least some of the first lenses            having an optical axis; and        -   a plurality of free-form lenses configured to direct the            collimated light beams from the plurality of first lenses            toward the vertical coupling elements at one or more angles            of incidence relative to a direction perpendicular to a main            surface of the photonic integrated circuit, wherein each            free-form lens has an optical axis, each of at least some of            the free-form lenses is asymmetric with respect to its            optical axis, each of at least some of the free-form lenses            has a focal point on its optical axis;    -   wherein each of at least some of the free-form lenses is        configured to receive light from a corresponding first lens, the        optical axis of the free-form lens is parallel to the optical        axis of the corresponding first lens, and the optical axis of        the free-form lens is spaced apart at a first distance relative        to the optical axis of the first lens.

Embodiment 63: The apparatus of embodiment 62 in which the plurality offree-form lenses are configured to direct the collimated light beamsfrom the plurality of first lenses toward the vertical coupling elementsat one or more angles of incidence in a range from 1° to 30° relative tothe direction perpendicular to the main surface of the photonicintegrated circuit.

Embodiment 64: The apparatus of embodiment 63 in which the plurality ofoptical fibers are arranged in a two-dimensional array.

Embodiment 65: The apparatus of embodiment 64 in which thetwo-dimensional array comprises at least 2 rows and at least 8 columns.

Embodiment 66: The apparatus of embodiment 65 in which the spacingbetween two adjacent rows in the two-dimensional array is identical tothe spacing between two adjacent columns in the two-dimensional array.

Embodiment 67: The apparatus of any of embodiments 62 to 66 in whicheach of at least some of the free-form off-axis lenses has a surfaceprofile that is configured to focus the light beam to a first locationon the vertical coupling element, the free-form off-axis lens has anoptical axis that passes the first location.

Embodiment 68: The apparatus of any of embodiments 62 to 67 in which atleast two free-form lenses are spaced apart at a second distance in arange from 1.5 to 4.5 times the first distance between the optical axisof the first lens and the optical axis of the free-form lens, the seconddistance represents the distance between the optical axes of thefree-form lenses, the first and second distances being measured along aplane parallel to the main surface of the photonic integrated circuit.

Embodiment 69: The apparatus of embodiment 68 in which the seconddistance is in a range from 2 to 3.5 times the first distance.

Embodiment 70: The apparatus of embodiment 69 in which the seconddistance is in a range from 2 to 3 times the first distance.

Embodiment 71: The apparatus of any of embodiments 62 to 70 in which theplurality of free-form lenses comprise an array of circularly free-formlenses, and each of at least some of the free-form lenses is spacedapart from a neighboring free-form lens at a second distance in a rangefrom 1.5 to 4.5 times the first distance between the optical axis of thefirst lens and the optical axis of the free-form lens.

Embodiment 72: The apparatus of embodiment 71 in which the seconddistance is in a range from 2 to 3.5 times the first distance.

Embodiment 73: The apparatus of embodiment 72 in which the seconddistance is in a range from 2 to 3 times the first distance.

Embodiment 74: The apparatus of any of embodiments 62 to 73 in which thefirst axis and the optical axis are perpendicular to the main surface ofthe photonic integrated circuit.

Embodiment 75: The apparatus of any of embodiments 62 to 74 in whicheach of at least some of the free-form lenses and the correspondingfirst lens are positioned relative to the vertical coupling element suchthat the first distance between the optical axis of the first lens andthe optical axis of the free-form lens is in a range from 10% to 150% ofthe full width at half maximum of the light beam received at thefree-form lens.

Embodiment 76: The apparatus of embodiment 75 in which each of at leastsome of the free-form lenses and the corresponding first lens arepositioned relative to the vertical coupling element such that the firstdistance between the optical axis of the first lens and the optical axisof the free-form lens is in a range from 20% to 80% of the full width athalf maximum of the light beam received at the free-form lens.

Embodiment 77: The apparatus of any of embodiments 62 to 76 in whicheach of at least some of the free-form lenses and the correspondingfirst lens are positioned relative to the vertical coupling element suchthat the portion of the light beam received at the free-form lens havingan intensity greater than half maximum is entirely offset from theoptical axis of the free-form lens.

Embodiment 78: The apparatus of any of embodiments 62 to 77 in whicheach of at least some of the free-form lenses comprises a truncatedversion of a rotationally symmetric optical lens, the optical axis ofthe free-form optical lens overlaps the optical axis of the rotationallysymmetric optical lens, and the free-form lens is asymmetric withrespect to the optical axis.

Embodiment 79: The apparatus of embodiment 78 in which the free-formlens has a dimension that is less than 1.5 times the radius of therotationally symmetric optical lens, the dimension of the free-form lensand the radius of the rotationally symmetric optical lens are measuredalong a plane parallel to the main surface of the photonic integratedcircuit.

Embodiment 80: The apparatus of embodiment 79 in which the free-formlens has a dimension that is less than 1.2 times the radius of therotationally symmetric optical lens.

Embodiment 81: The apparatus of any of embodiments 78 to 80 in whicheach of at least some of the free-form lenses has a footprint that isless than 50% of a footprint of the corresponding rotationally symmetricoptical lens.

Embodiment 82: The apparatus of any of embodiments 62 to 81 in whicheach of at least some of the free-form lenses has a dimension that isless than 1.5 times the diameter of the light beam received at thefree-form lens, and the diameter of the light beam is the full width athalf maximum of the light beam.

Embodiment 83: The apparatus of embodiment 82 in which each of at leastsome of the free-form lenses has a footprint having an area that is lessthan 2.25 times the area of the cross section of the light beam receivedat the free-form lens, and the area of the cross section of the lightbeam is calculated based on the full width at half maximum of the lightbeam.

Embodiment 84: The apparatus of any of embodiments 62 to 83 in which thefirst lenses are configure to collimate light from optical fibers havingend facets that are polished at an angle in a range from 1 to 30 degreesrelative to a plane that is perpendicular to the optical axes of theoptical fibers.

Embodiment 85: The apparatus of embodiment 84 in which the first lensesare configure to collimate light from optical fibers having end facetsthat are polished at an angle in a range from 4 to 15 degrees relativeto the plane that is perpendicular to the optical axes of the opticalfibers.

Embodiment 86: The apparatus of embodiment 85 in which the first lensesare configure to collimate light from optical fibers having end facetsthat are polished at an angle in a range from 6 to 10 degrees relativeto the plane that is perpendicular to the optical axes of the opticalfibers.

Embodiment 87: The apparatus of any of embodiments 84 to 86 in which thefirst lenses comprises a second plurality of free-form lenses configuredto optically couple the optical fibers to the first plurality offree-form lenses.

Embodiment 88: The apparatus of embodiment 87 in which the secondplurality of free-form lenses have surface profiles that aresubstantially similar to the first plurality of free-form lenses.

Embodiment 89: The apparatus of any of embodiments 62 to 88 in which thefirst plurality of free-form lenses are configured to direct lighttoward, or receive light from, the vertical coupling elements at one ormore angles of incidence in a range from 4° to 15° relative to thedirection perpendicular to the main surface of the photonic integratedcircuit.

Embodiment 90: The apparatus of embodiment 89 in which the firstplurality of circularly asymmetric optical lenses are configured todirect light toward, or receive light from, the vertical couplingelements at one or more angles of incidence in a range from 5° to 12°relative to the direction perpendicular to the main surface of thephotonic integrated circuit.

Embodiment 91: The apparatus of embodiment 90 in which the firstplurality of free-form lenses are configured to direct light toward, orreceive light from, the vertical coupling elements at one or more anglesof incidence in a range from 6° to 10° relative to the directionperpendicular to the main surface of the photonic integrated circuit.

Embodiment 92: The apparatus of embodiment 91 in which the plurality offree-form lenses are configured to direct light toward, or receive lightfrom, the vertical coupling elements at one or more offset angles in arange from 7° to 9° relative to the direction perpendicular to the mainsurface of the photonic integrated circuit.

Embodiment 93: The apparatus of any of embodiments 62 to 92 in whicheach of at least some of the free-form lenses has a circular or ovalcircumference.

Embodiment 94: The apparatus of any of embodiments 62 to 93 in whicheach of at least some of the free-form lenses has a polygonalcircumference.

Embodiment 95: The apparatus of any of embodiments 62 to 94 in which atleast some of the free-form lenses have a same shape.

Embodiment 96: The apparatus of any of embodiments 62 to 95 in which theplurality of free-form lenses comprise an array of rows and columns offree-form lenses.

Embodiment 97: The apparatus of any of embodiments 62 to 96, comprisingthe photonic integrated circuit.

Embodiment 98: The apparatus of any of embodiments 62 to 97, comprisinga first connector element configured to be mechanically and opticallycoupled to a second connector element that is optically coupled to theplurality of optical fibers.

Embodiment 99: The apparatus of any of embodiments 62 to 98 in which thevertical coupling elements comprise vertical grating couplers.

Embodiment 100: The apparatus of any of embodiments 62 to 99 in whichthe plurality of free-form lenses comprise silicon lenses.

Embodiment 101: The apparatus of any of embodiments 97 to 100 in whichthe photonic integrated circuit comprises optical waveguides that arecoupled to the vertical coupling elements.

Embodiment 102: The apparatus of any of embodiments 62 to 101 in whichthe fiber-optic connector comprises one or more walk-off elementsconfigured to receive input optical beams from one or more of the fibercores, and separate each of at least some of the input optical beamsinto a first optical beam component having a first polarization and asecond optical beam component having a second polarization, and

-   -   a birefringent plate having holes, in which the birefringent        plate is positioned relative to the one or more walk-off        elements such that each of at least some of the holes is aligned        with a corresponding first optical beam component, wherein the        birefringent plate rotates a polarization of each of at least        some of the of the second optical beam components to cause the        second optical beam component to have a same polarization as the        corresponding first optical beam component.

Embodiment 103: The apparatus of embodiment 102 in which the pluralityof first free-form lenses comprise a plurality of pairs of free-formlenses, each of at least some of the pairs of free-form lenses areconfigured to couple corresponding first and second optical beamcomponents to a pair of vertical coupling elements.

Embodiment 104: The apparatus of embodiment 102 or 103 in which theholes comprise at least one of circular holes, square holes, rectangularholes, or strip holes.

Embodiment 105: The apparatus of any of embodiments 62 to 104 in which adistance between two adjacent optical fibers is in a range from 225 μmto 275 μm, and a distance between two adjacent circularly asymmetricoptical lenses is in a range from 100√{square root over (2)} μm to150√{square root over (2)} μm.

Embodiment 106: A data center comprising the apparatus of any ofembodiments 54 to 105.

Embodiment 107: A method of operating the apparatus of any ofembodiments 54 to 105.

Embodiment 108: A method of operating the data center of embodiment 106.

Embodiment 109: A method of assembly the apparatus of any of embodiments54 to 105.

Embodiment 110: A method of processing data using the apparatus of anyof embodiments 54 to 105.

Embodiment 111: A method comprising:

-   -   transmitting light from a plurality of optical fibers to a        plurality of first lenses;    -   directing a plurality of light beams from the plurality of first        lenses to a plurality of circularly asymmetric optical lenses;        and    -   directing, using the circularly asymmetric optical lenses, the        plurality of light beams toward a plurality of vertical coupling        elements on a photonic integrated circuit at one or more angles        of incidence relative to a direction perpendicular to a main        surface of the photonic integrated circuit.

Embodiment 112: The method of embodiment 111 in which directing theplurality of light beams toward the plurality of vertical couplingelements comprises directing the plurality of light beams toward theplurality of vertical coupling elements at one or more angles ofincidence in a range from 1° to 30° relative to the directionperpendicular to the main surface of the photonic integrated circuit.

Embodiment 113: The apparatus of embodiment 112 in which the pluralityof optical fibers are arranged in a two-dimensional array.

Embodiment 114: The method of embodiment 113 in which thetwo-dimensional array comprises at least 2 rows and at least 8 columns.

Embodiment 115: The method of any of embodiments 112 to 114 in which thespacing between two adjacent rows in the two-dimensional array isidentical to the spacing between two adjacent columns in thetwo-dimensional array.

Embodiment 116: The method of any of embodiments 111 to 115 in whicheach of at least some of the circularly asymmetric optical lensescomprises a truncated version of a rotationally symmetric optical lens,the optical axis of the circularly asymmetric optical lens overlaps theoptical axis of the rotationally symmetric optical lens, and thecircularly asymmetric optical lens is asymmetric with respect to theoptical axis.

Embodiment 117: The method of any of embodiments 111 to 116 in whichtransmitting light from a plurality of optical fibers to a plurality offirst lenses comprises transmitting light from a plurality of opticalfibers with a θ degree polish, 0<θ<30° to a second plurality ofcircularly asymmetric lenses.

Embodiment 118: The method of any of embodiments 111 to 117 in whichtransmitting a plurality of light beams from the plurality of firstlenses to a plurality of circularly asymmetric optical lenses comprisestransmitting a plurality of collimated light beams from the plurality offirst lenses to the plurality of circularly asymmetric optical lenses.

Embodiment 119: A method comprising:

-   -   transmitting light from a plurality of optical fibers to a        plurality of first lenses;    -   directing a plurality of light beams from the plurality of first        lenses to a plurality of circularly asymmetric optical lenses;        and    -   directing, using the plurality of circularly asymmetric optical        lenses, the light beams to a plurality of vertical coupling        elements on a photonic integrated circuit, comprising:        -   directing, using each of at least some of the circularly            asymmetric optical lenses, a light beam towards the            corresponding vertical coupling element at an angle of            incidence relative to a direction perpendicular to a main            surface of the photonic integrated circuit;    -   wherein each of at least some of the circularly asymmetric        optical lenses is asymmetric with respect to an optical axis        that is perpendicular to the main surface of the photonic        integrated circuit.

Embodiment 120: The method of embodiment 119 in which directing thelight beam towards the corresponding vertical coupling element comprisesdirecting the light beam towards the corresponding vertical couplingelement at an angle of incidence in a range from 10 to 300 relative tothe direction perpendicular to the main surface of the photonicintegrated circuit.

Embodiment 121: A method comprising:

-   -   transmitting light from a plurality of optical fibers to a        plurality of first lenses;    -   directing a plurality of light beams from the plurality of first        lenses to a plurality of free-form lenses; and    -   directing, using the free-form lenses, the plurality of light        beams toward a plurality of vertical coupling elements on a        photonic integrated circuit at one or more angles of incidence        relative to a direction perpendicular to a main surface of the        photonic integrated circuit.

Embodiment 122: The method of embodiment 121 in which directing theplurality of light beams toward the plurality of vertical couplingelements comprises directing the plurality of light beams toward theplurality of vertical coupling elements at one or more angles ofincidence in a range from 1° to 30° relative to the directionperpendicular to the main surface of the photonic integrated circuit.

Embodiment 123: A method comprising:

-   -   transmitting light from a two-dimensional array of optical        fibers to a two-dimensional array of first lenses, wherein each        first lens has an optical axis;    -   directing a plurality of collimated light beams from the        two-dimensional array of first lenses to a two-dimensional array        of free-form lenses; and    -   directing, using a two-dimensional array of free-form lenses,        the collimated light beams from the array of first lenses toward        a two-dimensional array of vertical grating couplers on a        photonic integrated circuit at one or more angles of incidence        relative to a direction perpendicular to a main surface of the        photonic integrated circuit,    -   wherein each free-form lens has an optical axis, each of at        least some of the free-form lenses is asymmetric with respect to        its optical axis, and each of at least some of the free-form        lenses has a focal point on its optical axis;    -   wherein each of at least some of the free-form lenses receives a        collimated light beam from a corresponding first lens, the        optical axis of the free-form lens is parallel to the optical        axis of the corresponding first lens, and the optical axis of        the free-form lens is spaced apart at a first distance relative        to the optical axis of the first lens.

Embodiment 124: The method of embodiment 123 in which directing thecollimated light beams from the array of first lenses toward thetwo-dimensional array of vertical grating couplers comprises directingthe collimated light beams from the array of first lenses toward thetwo-dimensional array of vertical grating couplers at one or more anglesof incidence in a range from 1° to 30° relative to the directionperpendicular to the main surface of the photonic integrated circuit.

Embodiment 125: The apparatus of any of embodiments 1 to 48, 54 to 105,and 123 in which the fiber-optic connector comprises a second pluralityof circularly asymmetric optical lenses or a second plurality offree-form lenses that are not used to direct any light beam towards anyvertical coupling element.

Embodiment 126: The apparatus of any of embodiments 8 to 48 in which theoffset distance between the first axis of the light beam and the opticalaxis of the circularly asymmetric optical lens is at least 10 μm.

Embodiment 127: The apparatus of any of embodiments 8 to 48 in which theoffset distance between the first axis of the light beam and the opticalaxis of the circularly asymmetric optical lens is at least 20 μm.

Embodiment 128: The apparatus of any of embodiments 8 to 48 in which theoffset distance between the first axis of the light beam and the opticalaxis of the circularly asymmetric optical lens is at least 40 μm.

Embodiment 129: The apparatus of any of embodiments 62 to 105 and 123 inwhich the distance between the optical axis of the first lens and theoptical axis of the free-form lens is at least 10 μm.

Embodiment 130: The apparatus of any of embodiments 62 to 105 and 123 inwhich the distance between the optical axis of the first lens and theoptical axis of the free-form lens is at least 20 μm.

Embodiment 131: The apparatus of any of embodiments 62 to 105 and 123 inwhich the distance between the optical axis of the first lens and theoptical axis of the free-form lens is at least 40 μm.

The following is a fourth set of embodiments. The embodiment numbersbelow refer to those in the fourth set of embodiments.

Embodiment 1: An apparatus comprising:

-   -   one or more optical fibers having a plurality of fiber cores;    -   a photonic integrated circuit including a plurality of        vertical-coupling elements disposed along a main surface of the        photonic integrated circuit; and    -   a fiber-optic connector connected between the one or more        optical fibers and the photonic integrated circuit to        communicate light between the one or more optical fibers and the        photonic integrated circuit, wherein the fiber-optic connector        comprises a polarization beam splitter and a patterned        birefringent plate;    -   wherein the polarization beam splitter is configured to split an        incident light beam from a corresponding fiber core into a first        beam having a first polarization and a second beam having a        second polarization different from the first polarization;    -   wherein the patterned birefringent plate comprises a first        region and a second region, the first region has a first optical        birefringence, the second region has a second optical        birefringence that is different from the first optical        birefringence, the first region is produced by applying        localized heating to a portion of a birefringent plate to reduce        the birefringence at the first region, the second region is not        subject to the localized heating and retains its original        birefringence;    -   wherein the polarization beam splitter is configured to direct        the first beam towards the first region and direct the second        beam towards the second region;    -   wherein the first region is configured to rotate the        polarization of the first beam by a first amount, the second        region is configured to rotate the polarization of the second        beam by a second amount that is different from the first amount,        the first and second amounts are selected to cause the first and        second beams to have substantially parallel polarization after        passing the patterned birefringent plate.

Embodiment 2: The apparatus of embodiment 1 in which the patternedbirefringent plate is made from a single piece of birefringent material.

Embodiment 3: The apparatus of embodiment 1 or 2 in which the firstregion is an integral portion of the patterned birefringent plate, andno glue or adhesive is used to bond the first region to other portionsof the patterned birefringent plate.

Embodiment 4: The apparatus of any of embodiments 1 to 3 in which thepatterned birefringent plate has a top surface and a bottom surface, andthe first region extends from the top surface to the bottom surface.

Embodiment 5: The apparatus of any of embodiments 1 to 3 in which thepatterned birefringent plate has a top surface and a bottom surface, thefirst region is positioned within the birefringent plate at a firstdistance from the top surface and a second distance from the bottomsurface.

Embodiment 6: The apparatus of any of embodiments 1 to 3 in which thepatterned birefringent plate has a top surface and a bottom surface, thefirst region extends from the top surface to a location within thebirefringent plate at a distance from the bottom surface.

Embodiment 7: The apparatus of any of embodiments 1 to 6 in which thepolarization beam splitter is configured to cause the secondpolarization of the second beam to be orthogonal to the firstpolarization of the first beam after the first and second beams exit thepolarization beam splitter;

-   -   wherein the first region has substantially zero birefringence,        and the second region is configured to rotate the polarization        of the second beam by about 90°+n×180°, 0≤n, n being an integer.

Embodiment 8: The apparatus of any of embodiments 1 to 7 in which theone or more optical fibers comprise an array of at least 2 rows and atleast 8 columns of fiber cores;

-   -   wherein the patterned birefringent plate comprises at least two        first regions, each first region has an elongated shape that        extends along a direction parallel to the row direction;    -   wherein the second region comprises the birefringent material        adjacent to the first regions;    -   wherein the polarization beam splitter is configured to split 8        incident light beams from 8 corresponding fiber cores of a row        into 8 first beams having the first polarization and 8 second        beams having the second polarization, direct the 8 first beams        toward a first region, and direct the 8 second beams to the        second region;    -   wherein upon the 8 first beams passing through the first region        and the 8 second beams passing through the second region, the 8        first beams and the 8 second beams have substantially parallel        polarization.

Embodiment 9: The apparatus of any of embodiments 1 to 7 in which theone or more optical fibers comprise an array of at least 2 rows and atleast 8 columns of fiber cores;

-   -   wherein the patterned birefringent plate comprises an array of        at least 2 rows and at least 8 columns of first regions;    -   wherein the second region comprises the birefringent material        adjacent to the first regions;    -   wherein the polarization beam splitter is configured to split 8        incident light beams from 8 corresponding fiber cores of a row        into 8 first beams having the first polarization and 8 second        beams having the second polarization different from the first        polarization, direct the 8 first beams toward 8 corresponding        first regions, and direct the 8 second beams towards the second        region;    -   wherein upon the 8 first beams passing through the 8 first        regions and the 8 second beams passing through the second        region, the 8 first beams and the 8 second beams have        substantially parallel polarization.

Embodiment 10: The apparatus of any of embodiments 1 to 9 in which thefiber-optic connector comprises a first connector part and a secondconnector part, the first connector part is removably coupled to thesecond connector part, the first connector part is optically coupled tothe plurality of fiber cores, the second connector part is opticallycoupled to the plurality of vertical-coupling elements, and both thepolarization beam splitter and the patterned birefringent plate areincluded in the first connector part.

Embodiment 11: The apparatus of any of embodiments 1 to 9 in which thefiber-optic connector comprises a first connector part and a secondconnector part, the first connector part is removably coupled to thesecond connector part, the first connector part is optically coupled tothe plurality of fiber cores, the second connector part is opticallycoupled to the plurality of vertical-coupling elements, and both thepolarization beam splitter and the patterned birefringent plate areincluded in the second connector part.

Embodiment 12: The apparatus of any of embodiments 1 to 9 in which thefiber-optic connector comprises a first connector part and a secondconnector part, the first connector part is removably coupled to thesecond connector part, the first connector part is optically coupled tothe plurality of fiber cores, the second connector part is opticallycoupled to the plurality of vertical-coupling elements, the polarizationbeam splitter is included in the first connector part, and the patternedbirefringent plate is included in the second connector part.

Embodiment 12a: The apparatus of any of embodiments 1 to 12 in which thefirst region is configured to rotate the polarization of the first beamby an amount less than 5°.

Embodiment 12b: The apparatus of embodiment 12a in which the firstregion is configured to rotate the polarization of the first beam by anamount less than 1°.

Embodiment 12c: The apparatus of embodiment 12b in which the firstregion is configured to rotate the polarization of the first beam by anamount equal to zero.

Embodiment 13: An apparatus comprising:

-   -   a fiber-optic connector configured to be connected between one        or more optical fibers having a plurality of fiber cores and a        photonic integrated circuit including a plurality of        vertical-coupling elements disposed along a main surface of the        photonic integrated circuit, wherein the fiber-optic connector        comprises a polarization beam splitter and a patterned        birefringent plate;    -   wherein the polarization beam splitter is configured to split an        incident light beam from a corresponding fiber core into a first        beam having a first polarization and a second beam having a        second polarization different from the first polarization;    -   wherein the patterned birefringent plate comprises a first        region and a second region, the first region has a first optical        birefringence, the second region has a second optical        birefringence that is different from the first optical        birefringence, the difference in the first and second optical        birefringence is caused by performing at least one of (i)        applying localized heating to the first region without applying        localized heating to the second region to cause the first region        to have a lower birefringence as compared to the second region,        or (ii) applying different amounts of localized heating to the        first and second regions to cause the first region to have a        first birefringence and the second region to have a second        birefringence different from the first birefringence;    -   wherein the polarization beam splitter is configured to direct        the first beam towards the first region and direct the second        beam towards the second region;    -   wherein the first region is configured to rotate the        polarization of the first beam by a first amount, the second        region is configured to rotate the polarization of the second        beam by a second amount that is different from the first amount,        the first and second amounts are selected to cause the first and        second beams to have substantially parallel polarization after        passing the patterned birefringent plate.

Embodiment 14: The apparatus of embodiment Error! Reference source notfound. in which the first region is an integral portion of the patternedbirefringent plate, and no glue or adhesive is used to bond the firstregion to other portions of the patterned birefringent plate.

Embodiment 14a: The apparatus of embodiment 13 or 14 in which the firstregion is configured to rotate the polarization of the first beam by anamount less than 5°.

Embodiment 14b: The apparatus of embodiment 14a in which the firstregion is configured to rotate the polarization of the first beam by anamount less than 1°.

Embodiment 14c: The apparatus of embodiment 14b in which the firstregion is configured to rotate the polarization of the first beam by anamount substantially equal to zero.

Embodiment 15: An apparatus comprising:

-   -   a first connector part that is part of a fiber-optic connector        configured to be connected between one or more optical fibers        having a plurality of fiber cores and a photonic integrated        circuit including a plurality of vertical-coupling elements        disposed along a main surface of the photonic integrated        circuit, wherein the fiber-optic connector comprises a        polarization beam splitter, and the first connector part        comprises a patterned birefringent plate;    -   wherein the polarization beam splitter is configured to split an        incident light beam from a corresponding fiber core into a first        beam having a first polarization and a second beam having a        second polarization different from the first polarization;    -   wherein the patterned birefringent plate comprises non-uniform        birefringence produced by applying localized heating to the        birefringent plate to cause one or more regions of the        birefringent plate to have reduced birefringence as compared to        one or more other regions of the birefringent plate, resulting        in at least one lower-birefringence region and at least one        higher-birefringence region in the patterned birefringent plate;    -   wherein the polarization beam splitter is configured to direct        the first beam towards a lower-birefringence region in the        patterned birefringent plate and direct the second beam towards        a higher-birefringence region in the patterned birefringent        plate;    -   wherein the lower-birefringent region is configured to rotate        the polarization of the first beam by a first amount, the        higher-birefringent region is configured to rotate the        polarization of the second beam by a second amount that is        different from the first amount, the first and second amounts        are selected to cause the first and second beams to have        substantially parallel polarization after passing the patterned        birefringent plate.

Embodiment 16: The apparatus of embodiment 15 in which thelower-birefringence region has substantially zero birefringence.

Embodiment 17: The apparatus of embodiment 15 or 16 in which the firstconnector part comprises the polarization beam splitter.

Embodiment 18: The apparatus of any of embodiments 15 to 17 in which thelower-birefringence region is an integral portion of the patternedbirefringent plate, and no glue or adhesive is used to bond thelower-birefringence region to other portions of the patternedbirefringent plate.

Embodiment 19: An apparatus comprising:

-   -   a patterned birefringent plate that is part of a fiber-optic        connector configured to be connected between one or more optical        fibers having a plurality of fiber cores and a photonic        integrated circuit including a plurality of vertical-coupling        elements disposed along a main surface of the photonic        integrated circuit;    -   wherein the patterned birefringent plate comprises non-uniform        birefringence produced by applying localized heating to the        birefringent plate to cause one or more regions of the        birefringent plate to have reduced birefringence as compared to        one or more other regions of the birefringent plate, resulting        in at least one lower-birefringence region and at least one        higher-birefringence region in the patterned birefringent plate;    -   wherein the lower-birefringence region is configured to rotate        the polarization of a first light beam by a first amount, the        higher-birefringence region is configured to rotate the        polarization of a second light beam by a second amount that is        different from the first amount, the first and second light        beams are transmitted between one or more of the plurality of        fiber cores and one or more of the vertical-coupling elements.

Embodiment 20: The apparatus of embodiment 19 in which the fiber-opticconnector comprises a first connector part removably coupled to a secondconnector part, the first connector part optically coupled to theplurality of fiber cores, the second connector part coupled to thevertical coupling elements, and the first connector part comprises thepolarization beam splitter.

Embodiment 21: The apparatus of embodiment 19 or 20 in which thelower-birefringence region has substantially zero birefringence and isconfigured to rotate the polarization of a first light beam by asubstantially zero amount.

Embodiment 22: An apparatus comprising:

-   -   a fiber-optic connector configured to optically couple a        plurality of optical fibers to a plurality of vertical coupling        elements on a photonic integrated circuit, in which the        fiber-optic connector comprises:        -   a patterned birefringent plate comprising a plurality of            first regions and a plurality of second regions, the first            regions comprising a material having birefringence that is            different from the birefringence of the material of the            second regions, the first and second regions form an            integrated piece of optical element;    -   wherein the fiber-optic connector is configured to enable light        beams to be transmitted between the plurality of optical fibers        and the plurality of vertical coupling elements, and the        patterned birefringent plate is configured to modify an optical        property of a selected portion of light that passes through the        patterned birefringent plate.

Embodiment 23: The apparatus of embodiment 22 in which the patternedbirefringent plate is configured to modify the polarization of a firstportion of the light that passes through the patterned birefringentplate by a first amount, and modify the polarization of a second portionof the light that passes through the patterned birefringent plate by asecond amount.

Embodiment 24: An apparatus comprising:

-   -   a fiber-optic connector configured to optically couple a        plurality of optical fibers to a plurality of vertical coupling        elements on a photonic integrated circuit, in which the        fiber-optic connector comprises a patterned birefringent plate        comprising non-uniform birefringence produced by chemical        etching one or more portions of a birefringent plate to cause        the patterned birefringent plate to have one or more first        regions of birefringent material having a first thickness and        one or more second regions of birefringent material having a        second thickness that is different from the first thickness;    -   wherein the fiber-optic connector is configured to enable light        beams to be transmitted between the plurality of optical fibers        and the plurality of vertical coupling elements, and the        patterned birefringent plate is configured to modify an optical        property of a selected portion of light that passes through the        patterned birefringent plate.

Embodiment 25: The apparatus of embodiment 24 in which the first regionhas a dimension in a range from 50 μm to 1000 μm, the dimension ismeasured along a plane parallel to a top surface of the patternedbirefringent plate.

Embodiment 26: The apparatus of embodiment 25 in which the first regionhas a dimension in a range from 100 μm to 600 μm, the dimension ismeasured along a plane parallel to a top surface of the patternedbirefringent plate.

Embodiment 27: The apparatus of embodiment 26 in which the first regionhas a dimension in a range from 200 μm to 400 μm, the dimension ismeasured along a plane parallel to a top surface of the patternedbirefringent plate.

Embodiment 28: The apparatus of any of embodiments 24 to 27 in which thethickness of the birefringent material in the first region issubstantially zero.

Embodiment 29: The apparatus of any of embodiments 24 to 28 in which thepatterned birefringent plate is configured to modify a polarizationstate of a first set of light beams that pass through the first regionsrelative to a polarization state of a second set of light beams thatpass through the second regions of the birefringent plate.

Embodiment 30: A method comprising:

-   -   fabricating a fiber-optic connector, comprising applying        localized heating to a birefringent plate to produce a patterned        birefringent plate, in which the localized heating modifies        birefringence of a plurality of first regions in the        birefringent plate to cause the first regions to have        birefringence that is different from the birefringence of second        regions that do not receive the localized heating;    -   aligning the patterned birefringent plate to other optical        components in the fiber-optic connector; and    -   bonding the patterned birefringent plate to the other optical        components in the fiber-optic connector.

Embodiment 31: A method of fabricating a fiber-optic connector, themethod comprising:

-   -   applying localized heating to a birefringent plate to produce a        patterned birefringent plate, in which the localized heating        modifies birefringence of a plurality of first regions in the        birefringent plate to cause the first regions to have        birefringence that is different from the birefringence of second        regions that do not receive the localized heating; and    -   attaching the patterned birefringent plate to a second component        to form a fiber-optic connector that is configured to be coupled        to at least one of a plurality of optical fibers or a plurality        of coupling elements on a photonic integrated circuit.

Embodiment 32: The method of embodiment 31 in which the localizedheating causes the first regions to have reduced birefringence.

Embodiment 33: The method of embodiment 31 in which the localizedheating causes the first regions to have substantially zerobirefringence.

Embodiment 34: The method of any of embodiments 31 to 33 in whichapplying localized heating comprises applying a laser beam to the firstregions to locally heat the first regions.

Embodiment 35: The method of any of embodiments 31 to 34 in which thefirst regions comprise elongated strips, the elongated strips havelengthwise directions that are parallel to one another, and the stripsare spaced apart in a direction perpendicular to the lengthwisedirection.

Embodiment 36: The method of any of embodiments 31 to 34 in which thepatterned birefringent plate comprises an array of at least 2 rows andat least 8 columns of first regions.

Embodiment 37: The method of any of embodiments 31 to 36 in which priorto applying the localized heating, the birefringent plate comprises acrystalline quartz plate having predefined birefringence, and

-   -   the localized heating produces amorphous fused silica having        modified, lower, or substantially no birefringence in the first        regions.

Embodiment 38: The method of any of embodiments 31 to 37 in whichapplying localized heating comprises sequentially applying localizedheating to the first regions one after another.

Embodiment 39: The method of any of embodiments 31 to 37 in whichapplying localized heating comprises applying localized heating tomultiple first regions in parallel.

Embodiment 40: The method of any of embodiments 31 to 39 in which thebirefringent plate is configured to modify a polarization state of afirst set of light beams that pass through the first regions of thebirefringent plate relative to a polarization state of a second set oflight beams that pass through the second regions of the birefringentplate.

Embodiment 41: The method of any of embodiments 31 to 40 in whichapplying localized heating to the birefringent plate comprises applyinglocalized heating to the birefringent plate to modify birefringence of atwo-dimensional array of first regions in the birefringent plate tocause the array of first regions to have birefringence that is differentfrom the birefringence of second regions that do not receive thelocalized heating, and the two-dimensional array comprises at least 2rows and at least 8 columns.

Embodiment 42: The method of embodiment 41 in which the spacing betweentwo adjacent rows in the two-dimensional array is identical to thespacing between two adjacent columns in the two-dimensional array.

Embodiment 43: The method of embodiment 41 or 42 in which thefiber-optic connector is configured to be optically coupled to atwo-dimensional array of optical fibers.

Embodiment 44: The method of embodiment 43 in which the fiber-opticconnector is configured to enable a first set of light beams and asecond set of light beams to be transmitted between the two-dimensionalarray of optical fibers and a two-dimensional array of vertical couplingelements, and

-   -   the birefringent plate is configured to modify a polarization        state of the first set of light beams that pass through the        first regions of the birefringent plate relative to a        polarization state of the second set of light beams that pass        through the second regions of the birefringent plate.

Embodiment 45: The method of any of embodiments 41 to 44 in which thefiber-optic connector is configured to be optically coupled to atwo-dimensional array of vertical coupling elements on the photonicintegrated circuit.

Embodiment 46: The method of embodiment 45 in which the fiber-opticconnector is configured to enable a first set of light beams and asecond set of light beams to be transmitted between a two-dimensionalarray of optical fibers and the two-dimensional array of verticalcoupling elements, and

-   -   the birefringent plate is configured to modify a polarization        state of the first set of light beams that pass through the        first regions of the birefringent plate relative to a        polarization state of the second set of light beams that pass        through the second regions of the birefringent plate.

Embodiment 47: The method of any of embodiments 41 to 46 in which eachof at least some of the first regions has a substantially circular,oval, triangular, square, or rectangular shape.

Embodiment 48: The method of any of embodiments 41 to 46 in which thetwo-dimensional array of first regions comprise at least 2 parallelstrips, and applying localized heating to the birefringent platecomprises applying localized heating to modify birefringence of the atleast 2 parallel strips in the birefringent plate to cause the at least2 parallel strips to have birefringence that is different from thebirefringence of the second regions that do not receive the localizedheating.

Embodiment 49: The method of embodiment 48 in which each strip has awidth in a range from 50 μm to 1000 μm.

Embodiment 50: The method of embodiment 49 in which each strip has awidth in a range from 100 μm to 600 μm.

Embodiment 51: The method of embodiment 50 in which each strip has awidth in a range from 200 μm to 400 μm.

Embodiment 52: The method of any of embodiments 31 to 51 in which thefiber-optic connector is configured to be optically coupled to aplurality of vertical coupling elements on the photonic integratedcircuit, and the fiber-optic connector is configured to enable the firstset of light beams and the second set of light beams to be transmittedbetween the plurality of optical fibers and the plurality of verticalcoupling elements.

Embodiment 53: The method of any of embodiments 31 to 52 in whichapplying the localized heating to the birefringent plate comprisesapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions.

Embodiment 54: The method of embodiment 53 in which applying thelocalized heating to the birefringent plate comprises applying thelocalized heating to the birefringent plate to reduce the birefringenceat the first regions to substantially zero birefringence.

Embodiment 55: The method of any of embodiments 31 to 54 in whichapplying the localized heating to the birefringent plate comprisesapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions such that the second set of lightbeams that pass through the second regions have polarization that isrotated about 90°+n×180°, 0≤n, n being an integer, relative topolarization of the first set of light beams that pass through the firstregions.

Embodiment 56: The method of any of embodiments 31 to 55 in whichattaching the patterned birefringent plate to a second componentcomprising attaching the patterned birefringent plate to a walk-offelement that is configured to:

-   -   receive a plurality of light beams from the plurality of optical        fibers,    -   split the light beams into first beam components and second beam        components, the second beam components have polarization that is        orthogonal to the polarization of the first beam components,    -   direct the first beam components toward the first regions having        lower birefringence, and    -   direct the second beam components toward the second regions        having higher birefringence.

Embodiment 57: The method of embodiment 56 in which applying thelocalized heating to the birefringent plate comprises applying thelocalized heating to the birefringent plate to reduce the birefringenceat the first regions such that the second set of light beams that passthrough the second regions have polarization that is rotated about90°+n×180°, 0≤n, n being an integer, relative to polarization of thefirst set of light beams that pass through the first regions,

-   -   wherein the walk-off element is configured such that upon        exiting the walk-off element the first beam components have        first polarization, and the second beam components have second        polarization that is substantially orthogonal to the first        polarization,    -   wherein the first and second regions of the birefringent plate        are configured such that after passing the first and second        regions the first beam components have polarization that is        substantially parallel to the polarization of the second beam        components.

Embodiment 58: The method of embodiment 56 or 57 in which the walk-offelement is configured to separate the first beam component and thesecond beam component along a walk-off direction, each of at least someof the first regions has a dimension measured along a direction parallelto the walk-off direction in a range from 50 μm to 1000 μm.

Embodiment 59: The method of any of embodiments 31 to 58 in which eachof at least some of the first regions has a dimension measured along adirection parallel to the walk-off direction in a range from 100 μm to600 μm.

Embodiment 60: The method of embodiment 59 in which each of at leastsome of the first regions has a dimension measured along a directionparallel to the walk-off direction in a range from 200 μm to 400 μm.

Embodiment 61: The method of any of embodiments 31 to 60 in whichapplying localized heating to the birefringent plate comprises applyinglocalized heating to the birefringent plate to modify birefringence of atwo-dimensional pattern of first regions in the birefringent plate suchthat the birefringent plate is configured to modify polarization oflight passing the birefringent plate in a way that is equivalent tomodification of polarization of light passing a half-wave plate havingopenings at the two-dimensional pattern of first regions.

Embodiment 62: The method of any of embodiments 31 to 60 in which thebirefringent plate comprises a first surface and a second surface,

-   -   wherein applying localized heating to the birefringent plate        comprises applying localized heating to first regions that        extend from the first surface to the second surface.

Embodiment 63: The method of any of embodiments 31 to 60 in which thebirefringent plate comprises a first surface and a second surface,

-   -   wherein applying localized heating to the birefringent plate        comprises applying localized heating to first regions that are        positioned within the birefringent plate and spaced at a first        distance from the first surface and a second distance from the        second surface.

Embodiment 64: The method of any of embodiments 31 to 60 in which thebirefringent plate comprises a first surface and a second surface, thefirst surface is closer to the plurality of optical fibers relative tothe second surface,

-   -   wherein applying localized heating to the birefringent plate        comprises applying localized heating to first regions that        extend from the first surface to a location inside the        birefringent plate, the first regions are spaced at a distance        from the second surface.

Embodiment 65: The method of any of embodiments 31 to 60 in which thebirefringent plate comprises a first surface and a second surface, thefirst surface is closer to the plurality of coupling elements relativeto the second surface,

-   -   wherein applying localized heating to the birefringent plate        comprises applying localized heating to first regions that        extend from the second surface to a location inside the        birefringent plate, the first regions are spaced at a distance        from the first surface.

Embodiment 66: The method of any of embodiments 31 to 65 in whichapplying localized heating comprises using one or more laser beams toapply the localized heating.

Embodiment 67: A method of fabricating a fiber-optic connector, themethod comprising:

-   -   applying one or more particle beams to a birefringent plate to        locally energize regions of the birefringent plate to produce a        patterned birefringent plate, in which the localized energizing        modifies birefringence of a plurality of first regions in the        birefringent plate to cause the first regions to have        birefringence that is different from the birefringence of second        regions that do not receive the localized energizing; and    -   attaching the patterned birefringent plate to a second component        to form a fiber-optic connector that is configured to be coupled        to at least one of a plurality of optical fibers or a plurality        of coupling elements on a photonic integrated circuit.

Embodiment 68: A method of fabricating a fiber-optic connector, themethod comprising:

-   -   applying localized heating to a birefringent plate to modify        birefringence of a two-dimensional array of first regions in the        birefringent plate to cause the array of first regions to have        birefringence that is different from the birefringence of second        regions that do not receive the localized heating, the array        comprising at least 2 rows and at least 8 columns; and    -   coupling the birefringent plate to a first connector part and a        second connector part to form the fiber-optic connector, in        which the first connector part is configured to be coupled to a        plurality of optical fibers, the second connector part is        configured to be coupled to a photonic integrated circuit;    -   wherein the first optical connector part comprises a walk-off        element configured to:        -   receive a plurality of light beams from the plurality of            optical fibers,        -   split the light beams into first beam components and second            beam components, the second beam components having            polarization that is orthogonal to the polarization of the            first beam components,        -   direct the first beam components toward the first regions            having lower birefringence, and        -   direct the second beam components toward the second regions            having higher birefringence.

Embodiment 69: The method of embodiment 68 in which the birefringentplate is configured to modify a polarization state of the second beamcomponents that pass through the second regions of the birefringentplate relative to a polarization state of the first beam components thatpass through the first regions of the birefringent plate.

Embodiment 70: The method of embodiment 68 or 69 in which the secondconnector part is configured to be optically coupled to atwo-dimensional array of vertical coupling elements on the photonicintegrated circuit, and the fiber-optic connector is configured toenable light to be transmitted between the two-dimensional array ofoptical fibers and the two-dimensional array of vertical couplingelements.

Embodiment 71: The method of any of embodiments 68 to 70 in whichapplying the localized heating to the birefringent plate comprisesapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions.

Embodiment 72: The method of embodiment 71 in which applying thelocalized heating to the birefringent plate comprises applying thelocalized heating to the birefringent plate to reduce the birefringenceat the first regions to substantially zero birefringence.

Embodiment 73: The method of embodiment 71 or 72 in which applying thelocalized heating to the birefringent plate comprises applying thelocalized heating to the birefringent plate to reduce the birefringenceat the first regions such that the second beam components that passthrough the second regions have polarization that is rotated about90°+n×180°, 0≤n, n being an integer, relative to polarization of thefirst beam components that pass through the first regions.

Embodiment 74: The method of any of embodiments 68 to 73 in which thewalk-off element is configured such that upon exiting the walk-offelement the first beam components have first polarization, and thesecond beam components have second polarization that is substantiallyorthogonal to the first polarization,

-   -   wherein the first and second regions of the birefringent plate        are configured such that after passing the first and second        regions the first beam components have polarization that is        parallel to the polarization of the second beam components.

Embodiment 75: The method of any of embodiments 68 to 74 in which thewalk-off element separates the first beam component and the second beamcomponent along a walk-off direction, each of at least some of the firstregions has a dimension measured along a direction parallel to thewalk-off direction in a range from 50 μm to 1000 μm.

Embodiment 76: The method of embodiment 75 in which each of at leastsome of the first regions has a dimension measured along a directionparallel to the walk-off direction in a range from 100 μm to 600 μm.

Embodiment 77: The method of embodiment 76 in which each of at leastsome of the first regions has a dimension measured along a directionparallel to the walk-off direction in a range from 200 μm to 400 μm.

Embodiment 78: A method of fabricating a fiber-optic connector, themethod comprising:

-   -   applying localized heating or localized energizing to a        birefringent plate to modify birefringence of a plurality of        first regions in the birefringent plate to cause each of at        least some of the plurality of first regions to have a        birefringence that is different from the birefringence of second        regions that do not receive the localized heating or localized        energizing; and    -   attaching the birefringent plate to a first interface module and        a second interface module, in which the first interface module        is configured to be coupled to a plurality of optical fibers,        the second interface module is configured to be coupled to a        plurality of vertical coupling elements on a photonic integrated        circuit, the birefringent plate is positioned in optical paths        between the first interface module and the second interface        module, and the birefringent plate is configured to modify an        optical property of light differently depending on whether the        light passes through the first regions or the second regions.

Embodiment 79: The method of embodiment 78 in which the first interfacemodule is configured to be coupled to a two-dimensional array of opticalfibers, the two-dimensional array comprising at least 2 rows and atleast 8 columns, the second interface module is configured to be coupledto a two-dimensional array of vertical coupling elements, thebirefringent plate is configured to modify a polarization state of afirst set of light beams relative to a second set of light beams thatare transmitted between the two-dimensional array of optical fibers andthe two-dimensional array of vertical coupling elements.

Embodiment 80: The method of embodiment 79 in which after applyinglocalized heating or localized energizing to the birefringent plate, thebirefringent plate comprises a plurality of first regions that havelower birefringence and a plurality of second regions that have higherbirefringence, the first regions alternate with the second regions,

-   -   the first interface module comprises a walk-off element        configured to receive a plurality of light beams from the        plurality of optical fibers, split each of at least some of the        light beams into a first beam component and a second beam        component, direct the first beam component toward one of the        first regions having the lower birefringence, and direct the        second beam component toward one of the second regions having        the higher birefringence.

Embodiment 81: The method of embodiment 80 in which the walk-off elementis configured such that upon exiting the walk-off element the first beamcomponent has a first polarization, and the second beam component has asecond polarization that is orthogonal to the first polarization,

-   -   the first and second regions of the birefringent plate are        configured such that after passing the first and second regions        the first beam component has a polarization that is parallel to        the polarization of the second beam component.

Embodiment 82: The method of embodiment 80 in which the walk-off elementseparates the first beam component and the second beam component along awalk-off direction, each of at least some of the first regions has adimension measured along a direction parallel to the walk-off directionin a range from 50 μm to 1000 μm.

Embodiment 83: The method of embodiment 82 in which each of at leastsome of the first regions has a dimension measured along a directionparallel to the walk-off direction in a range from 100 μm to 600 μm.

Embodiment 84: The method of embodiment 83 in which each of at leastsome of the first regions has a dimension measured along a directionparallel to the walk-off direction in a range from 200 μm to 400 μm.

Embodiment 85: The method of embodiment 80 in which the walk-off elementis configured to direct a first beam component of a light beam to afirst region, direct a second beam component of the light beam to asecond region, and a center of the first region and a center of thesecond region are spaced apart at a distance in a range from 50 μm to1000 μm.

Embodiment 86: The method of embodiment 85 in which the center of thefirst region and the center of the second region are spaced apart at adistance in a range from 100 μm to 600 μm.

Embodiment 87: The method of embodiment 86 in which the center of thefirst region and the center of the second region are spaced apart at adistance in a range from 200 μm to 400 μm.

Embodiment 88: A method comprising:

-   -   generating a birefringent plate by performing:        -   attaching a birefringent element comprising an optically            birefringent material to a second optical element, and        -   applying a removal process to remove portions of the            optically birefringent material at a plurality of first            regions such that after the removal process the plurality of            first regions have no optically birefringent material or            have optically birefringent material with reduced thickness;            and    -   attaching the birefringent plate to a first connector part and a        second connector part to form the fiber-optic connector, in        which the first connector part is configured to be coupled to a        plurality of optical fibers, the second connector part is        configured to be coupled to a photonic integrated circuit, and        the birefringent plate is positioned between the first connector        part and the second connector part.

Embodiment 89: The method of embodiment 88 in which the birefringentplate is configured to modify a polarization state of a first set oflight beams that pass through the first regions to a polarization stateof a second set of light beams that pass through second regions of theoptically birefringent element that have optically birefringent materialwith an original thickness.

Embodiment 90: The method of embodiment 88 in which applying the removalprocess comprises etching the optical birefringent material at theplurality of first regions.

Embodiment 91: The method of embodiment 90, comprising disposing an etchstop layer between the optically birefringent element and the secondoptical element before etching the optical birefringent material,

-   -   wherein etching the optical birefringent material at the        plurality of first regions comprises etching the optical        birefringent element at the plurality of first regions until the        etch stop layer is reached.

Embodiment 92: The method of embodiment 91 in which the etch stop layercomprises an anti-reflective coating.

Embodiment 93: The method of embodiment 88 in which removing portions ofthe optically birefringent element comprises laser ablation of theoptical birefringent element at the plurality of first regions.

Embodiment 94: The method of embodiment 88 in which removing portions ofthe optically birefringent material comprises mechanical removal ofmaterial from the optical birefringent element at the plurality of firstregions.

Embodiment 95: The method of embodiment 88 in which removing portions ofthe optically birefringent material at the plurality of first regionscomprises removing portions of the optically birefringent material at atwo-dimensional array of first regions, the two-dimensional arraycomprises at least 2 rows and at least 8 columns.

Embodiment 96: The method of embodiment 95 in which the birefringentelement is attached to a first surface of the second optical element,

-   -   wherein each of the first regions has a shape substantially        resembling a circle, an oval, a triangle, a square, a rectangle,        or a polygon having n sides, n being an integer greater than 4,        and the shape is measured along a plane parallel to the first        surface of the second optical element.

Embodiment 97: The method of embodiment 95 in which each first regionhas a footprint that fits within a square having a side in a range from50 μm to 1000 μm.

Embodiment 98: The method of embodiment 97 in which each first regionhas a footprint that fits within a square having a side in a range from100 μm to 600 μm.

Embodiment 99: The method of embodiment 98 in which each first regionhas a footprint that fits within a square having a side in a range from200 μm to 400 μm.

Embodiment 100: The method of embodiment 88 in which the first opticalconnector part comprises a walk-off element configured to:

-   -   receive a plurality of light beams from the plurality of optical        fibers,    -   split the light beams into first beam components and second beam        components,    -   direct the first beam components toward the first regions, and    -   direct the second beam components toward second regions that are        not subject to the removal process.

Embodiment 101: The method of embodiment 100 in which applying theremoval process comprises removing the birefringent material or reducingthe height of the birefringent material at the first regions such thatthe second set of light beams that pass through the second regions havepolarization that is rotated about 90°+n×180°, 0≤n, n being an integer,relative to polarization of the first set of light beams that passthrough the first regions.

Embodiment 102: The method of embodiment 101 in which the walk-offelement is configured such that upon exiting the walk-off element thefirst beam components have first polarization, and the second beamcomponents have second polarization that is substantially orthogonal tothe first polarization,

-   -   wherein the first and second regions of the birefringent plate        are configured such that after passing the first and second        regions the first beam components have polarization that is        substantially parallel to the polarization of the second beam        components.

Embodiment 103: The method of embodiment 100 in which the walk-offelement separates the first beam component and the second beam componentalong a walk-off direction, each of at least some of the first regionshas a dimension measured along a direction parallel to the walk-offdirection in a range from 50 μm to 1000 μm.

Embodiment 104: The method of embodiment 103 in which each of at leastsome of the first regions has a dimension measured along a directionparallel to the walk-off direction in a range from 100 μm to 600 μm.

Embodiment 105: The method of embodiment 104 in which each of at leastsome of the first regions has a dimension measured along a directionparallel to the walk-off direction in a range from 200 μm to 400 μm.

Embodiment 106: The method of embodiment 88 in which applying theremoval process comprises applying the removal process to removeportions of the optically birefringent material at the first regionssuch that the birefringent plate is configured to modify polarization oflight passing through the birefringent plate in a way that is equivalentto modification of polarization of light passing through a half-waveplate having openings at the first regions.

Embodiment 107: The method of embodiment 88 in which generating thebirefringent plate comprises applying the removal process to generatestrips of birefringent material each having an original thickness, eachstrip has a width in a range from 50 μm to 1000 μm, and a length atleast 2000 μm.

Embodiment 108: The method of embodiment 107 in which each strip has awidth in a range from 100 μm to 600 μm, and a length at least 1200 μm.

Embodiment 109: The method of embodiment 108 in which each strip has awidth in a range from 200 μm to 400 μm, and a length at least 800 μm.

Embodiment 110: A method of fabricating a fiber-optic connector, themethod comprising:

-   -   applying a particle beam to locally energize portions of a        birefringent plate to generate a patterned birefringent plate by        modifying birefringence of a two-dimensional pattern of first        regions in the birefringent plate to cause the first regions to        have birefringence that is different from the birefringence of        second regions that do not receive the localized energizing by        the particle beam; and    -   coupling the patterned birefringent plate to a second component        to form the fiber-optic connector;    -   wherein the fiber-optic connector is configured to be coupled to        at least one of a plurality of optical fibers or a plurality of        vertical coupling elements on a photonic integrated circuit, and        the patterned birefringent plate comprises non-uniform        birefringence properties with respect to light that passes        through the patterned birefringent plate.

Embodiment 111: A method of fabricating fiber-optic connectors, themethod comprising:

-   -   providing a first module comprising a plurality of unsingulated        lens arrays;    -   providing a second module comprising a plurality of unsingulated        patterned birefringent plates, in which each patterned        birefringent plate comprises birefringent material, the        patterned birefringent plate comprises a plurality of first        regions having reduced or no birefringence as compared to a        plurality of second regions;    -   aligning the plurality of unsingulated lens arrays in the first        module to the plurality of unsingulated patterned birefringent        plates in the second module;    -   bonding the first module to the second module to form a first        assembly;    -   cutting the first assembly to singulate the first and second        modules to produce a plurality of fiber-optic connector parts,        in which each fiber-optic connector part comprises a singulated        birefringent plate and a singulated lens array.

Embodiment 112: A method of fabricating fiber-optic connectors, themethod comprising:

-   -   providing a first module comprising a plurality of unsingulated        first connector units, in which each first connector unit is        configured to be coupled to a plurality of optical fibers;    -   providing a second module comprising a plurality of unsingulated        patterned birefringent plates, in which each patterned        birefringent plate comprises birefringent material, the        patterned birefringent plate comprises a plurality of first        regions having reduced or no birefringence as compared to a        plurality of second regions, and the second module has a first        side and a second side;    -   aligning the plurality of unsingulated first connector units in        the first module to the plurality of unsingulated patterned        birefringent plates in the second module;    -   bonding the first module to the first side of the second module;    -   providing a third module comprising a plurality of unsingulated        second connector units, in which each second connector unit is        configured to be coupled to a photonic integrated circuit;    -   aligning the plurality of unsingulated second connector units in        the third module to the plurality of unsingulated patterned        birefringent plates in the second module;    -   bonding the third module to the second side of the second module        to form a first assembly; and    -   cutting the first assembly to singulate the first, second, and        third modules to produce a plurality of fiber-optic connectors,        in which each fiber-optic connector comprises:        -   a singulated birefringent plate,        -   a singulated first connector unit, and        -   a singulated second connector unit.

Embodiment 113: An apparatus comprising:

-   -   a fiber-optic connector configured to optically couple a        plurality of optical fibers to a plurality of vertical coupling        elements on a photonic integrated circuit, in which the        fiber-optic connector comprises a patterned birefringent plate        comprising an optically birefringent material, the birefringent        plate having a plurality of first regions that have        birefringence that is different from the birefringence of second        regions, the first regions are formed by localized heating or        localized energizing that modifies the birefringence of the        first regions, and the second regions are not subject to the        localized heating or localized energizing;    -   wherein the fiber-optic connector is configured to enable light        beams to be transmitted between the plurality of optical fibers        and the plurality of vertical coupling elements, and the        patterned birefringent plate is configured to modify an optical        property of a first set of the light beams relative to the        optical property of a second set of the light beams.

Embodiment 114: The apparatus of embodiment 113 in which the firstregions have reduced birefringence as compared to the second regions.

Embodiment 115: The apparatus of embodiment 114 in which the firstregions have substantially zero birefringence.

Embodiment 116: The apparatus of embodiment 113 in which the patternedbirefringent plate is configured to modify a polarization state of afirst set of light beams that pass through the first regions relative toa polarization state of a second set of light beams that pass throughthe second regions of the birefringent plate.

Embodiment 117: The apparatus of embodiment 113 in which the patternedbirefringent plate comprises a plurality of strips of birefringentmaterial that are spaced apart from one another, the first set of lightbeams pass through the plurality of strips of birefringent material, andthe second set of light beams pass through spacing between the pluralityof strips of birefringent material.

Embodiment 118: The apparatus of any of embodiments 113 to 117 in whichthe patterned birefringent element is configured to rotate thepolarization of the first set of the light beams relative to thepolarization of the second set of the light beams by an amountsubstantially equal to 90°+n×180°, 0≤n, n being an integer.

Embodiment 119: The apparatus of any of embodiments 113 to 118 in whichthe patterned birefringent element is configured to modify two lightbeams that have polarizations orthogonal to each other prior to passingthrough the patterned birefringent element such that the two light beamshave polarizations parallel to each other after passing through thepatterned birefringent element.

Embodiment 120: The apparatus of any of embodiments 113 to 118 in whichthe patterned birefringent element is configured to modify two lightbeams that have polarizations parallel to each other prior to passingthrough the patterned birefringent element such that the two light beamshave polarizations orthogonal to each other after passing through thepatterned birefringent element.

Embodiment 121: The apparatus of any of embodiments 113 to 120 in whichthe fiber-optic connector comprises one or more walk-off elementsconfigured to receive one or more input optical beams from one or moreof the optical fibers, and separate each of at least some of the inputoptical beams into a first optical beam component having a firstpolarization and a second optical beam component having a secondpolarization;

-   -   wherein the patterned birefringent element is configured to        modify the polarization of first optical beam component relative        to the polarization of second optical beam component such that        the polarization state of the first optical beam component        relative to the second optical beam component changes after the        first and second optical beam component pass through the        patterned birefringent element.

Embodiment 122: An apparatus comprising:

-   -   a fiber-optic connector configured to optically couple a        plurality of optical fibers to a plurality of vertical coupling        elements on a photonic integrated circuit, in which the        fiber-optic connector comprises a volume of birefringent        material, one or more portions of the volume of birefringent        material has or have modified birefringence compared to other        portions of the volume of birefringent material, and light beams        transmitted between the plurality of optical fibers and the        plurality of vertical coupling elements pass through the volume        of birefringent material;    -   wherein the volume of birefringent material is configured to        modify a polarization state of a first set of the light beams        relative to a second set of the light beams such that the        polarization state of the first set of the light beams relative        to the second set of the light beams changes after the first and        second sets of light beams pass through the volume of        birefringent material.

Embodiment 123: The apparatus of embodiment 122 in which the volume ofbirefringent material comprises a plurality of strips of birefringentmaterial that are spaced apart from one another, the first set of lightbeams pass through the plurality of strips of birefringent material, andthe second set of light beams pass through spacing between the pluralityof strips of birefringent material.

Embodiment 124: The apparatus of embodiment 122 or 123 in which thepatterned birefringent element is configured to rotate the polarizationof the first set of the light beams relative to the polarization of thesecond set of the light beams by an amount substantially equal to90°+n×180°, 0≤n, n being an integer.

Embodiment 125: The apparatus of any of embodiments 122 to 124 in whichthe patterned birefringent element is configured to modify two lightbeams that have polarizations orthogonal to each other prior to passingthrough the patterned birefringent element such that the two light beamshave polarizations parallel to each other after passing through thepatterned birefringent element.

Embodiment 126: The apparatus of any of embodiments 122 to 124 in whichthe patterned birefringent element is configured to modify two lightbeams that have polarizations parallel to each other prior to passingthrough the patterned birefringent element such that the two light beamshave polarizations orthogonal to each other after passing through thepatterned birefringent element.

Embodiment 127: The apparatus of any of embodiments 122 to 126 in whichthe fiber-optic connector comprises one or more walk-off elementsconfigured to receive one or more input optical beams from one or moreof the optical fibers, and separate each of at least some of the inputoptical beams into a first optical beam component having a firstpolarization and a second optical beam component having a secondpolarization;

-   -   wherein the patterned birefringent element is configured to        modify the polarization of first optical beam component relative        to the polarization of second optical beam component such that        the polarization state of the first optical beam component        relative to the second optical beam component changes after the        first and second optical beam component pass through the        patterned birefringent element.

Embodiment 128: The apparatus of any of embodiments 13 to 29 and 113 to127, comprising the photonic integrated circuit.

Embodiment 129: The apparatus of any of embodiments 1 to 29 and 113 to127 in which the vertical coupling elements comprise vertical gratingcouplers.

Embodiment 130: The method of any of embodiments 30 to 112 in which thevertical coupling elements comprise vertical grating couplers.

Embodiment 131: The apparatus of any of embodiments 1 to 29 and 113 to127 in which the photonic integrated circuit comprises opticalwaveguides that are coupled to the vertical coupling elements.

Embodiment 132: A data center comprising the apparatus of any ofembodiments 1 to 29 and 113 to 127.

Embodiment 133: A method of operating the apparatus of any ofembodiments 1 to 29 and 113 to 127.

Embodiment 134: A method of operating the data center of embodiment 132.

Embodiment 135: A method of assembly the apparatus of any of embodiments1 to 29 and 113 to 127.

Embodiment 136: A method of processing data using the apparatus of anyof embodiments 1 to 29 and 113 to 127.

Embodiment 137: A method comprising:

-   -   transmitting light from a plurality of optical fiber cores to a        polarization beam splitter;    -   at the polarization beam splitter, splitting an incident light        beam from a corresponding fiber core into a first beam having a        first polarization and a second beam having a second        polarization different from the first polarization;    -   directing the first and second beams toward a patterned        birefringent plate comprising a first region and a second        region, in which the first region has a first optical        birefringence, the second region has a second optical        birefringence that is different from the first optical        birefringence, the first region is produced by applying        localized heating to a portion of a birefringent plate to reduce        the birefringence at the first region, the second region is not        subject to the localized heating and retains its original        birefringence, the first beam is directed towards the first        region, the second beam is directed towards the second region;    -   at the first and second regions, rotating the polarization of        the first beam by a first amount and rotating the polarization        of the second beam by a second amount that is different from the        first amount, the first and second amounts are selected to cause        the first and second beams to have substantially parallel        polarization after passing the patterned birefringent plate.

Embodiment 138: The apparatus of embodiment 137 in which the pluralityof optical fiber cores are arranged in a two-dimensional array.

Embodiment 139: The method of embodiment 138 in which thetwo-dimensional array comprises at least 2 rows and at least 8 columns.

Embodiment 140: The method of any of embodiments 137 to 139 in which thespacing between two adjacent rows in the two-dimensional array isidentical to the spacing between two adjacent columns in thetwo-dimensional array.

The following is a fifth set of embodiments. The embodiment numbersbelow refer to those in the fifth set of embodiments.

Embodiment 1: A method comprising:

-   -   providing a photonic integrated circuit including a plurality of        vertical-coupling elements disposed along a main surface of the        photonic integrated circuit;    -   attaching an optical subassembly to the photonic integrated        circuit;    -   removably connecting a fiber connector to a ferrule frame,        wherein the fiber connector is attached to an array of optical        fibers;    -   aligning the ferrule frame to the optical subassembly using an        active alignment process; and    -   securely connecting the ferrule frame to the optical subassembly        after the active alignment process.

Embodiment 2: The method of embodiment 1 wherein the active alignmentprocess comprises:

-   -   transferring light between at least one optical fiber in the        array of optical fibers and the photonic integrated circuit        through the optical subassembly and at least one of the        vertical-coupling elements, and    -   adjusting a position of the ferrule frame relative to the        optical subassembly based on at least one characteristic of the        light transferred between the at least one optical fiber and the        photonic integrated circuit.

Embodiment 3: The method of embodiment 1 or 2, comprising removing thefiber connector from the ferrule frame.

Embodiment 4: The method of embodiment 1 or 3 wherein the ferrule framecomprises an opening to allow light from the array of optical fibers tobe transmitted to the optical subassembly.

Embodiment 5: The method of embodiment 4, comprising passing a portionof the fiber connector through the opening of the ferrule frame andpositioning an end of the fiber connector in proximity to the opticalsubassembly.

Embodiment 6: The method of any of embodiments 1 to 5 wherein removablyconnecting the array of optical fibers to the ferrule frame comprises atleast one of (i) using one or more screws to secure the array of opticalfibers to the ferrule frame, (ii) using one or more clamps to secure thearray of optical fibers to the ferrule frame, (iii) using one or moremagnets to connect the array of optical fibers to the ferrule frame.

Embodiment 7: The method of any of embodiments 1 to 6 wherein the arrayof optical fibers comprises a two-dimensional array of optical fibers.

Embodiment 8: The method of embodiment 7 wherein the two-dimensionalarray of optical fibers comprises at least two rows of optical fibers.

Embodiment 9: The method of any of embodiments 1 to 8 wherein the arrayof optical fibers comprise at least 10 fiber cores.

Embodiment 10: The method of embodiment 9 wherein the array of opticalfibers comprise at least 50 fiber cores.

Embodiment 11: The method of embodiment 10 wherein the array of opticalfibers comprise at least 100 fiber cores.

Embodiment 12: The method of any of embodiments 1 to 11 wherein theoptical subassembly comprises a first lens array, and the activealignment process comprises projecting light from the array of opticalfibers through the first lens array, including passing light from atleast one of the optical fibers through a corresponding lens to acorresponding vertical-coupling element.

Embodiment 13: The method of embodiment 12 wherein the opticalsubassembly comprises a beam displacer, and the active alignment processcomprises projecting light from the array of optical fibers through thefirst lens array and the beam displacer to the at least onevertical-coupling element.

Embodiment 14: The method of embodiment 13 wherein the opticalsubassembly comprises a second lens array, and the active alignmentprocess comprises projecting light from the array of optical fibersthrough the first lens array, the beam displacer, and the second lensarray to the at least one vertical-coupling element.

Embodiment 15: The method of embodiment 14 wherein the opticalsubassembly comprises a half wave plate, and the active alignmentprocess comprises projecting light from the array of optical fibersthrough the first lens array, the beam displacer, the half wave plate,and the second lens array to the at least one vertical-coupling element.

Embodiment 16: The method of any of embodiments 1 to 11 wherein thefiber connector comprises a first lens array, and the active alignmentprocess comprises projecting light from the array of optical fibersthrough the first lens array, including passing light from at least oneof the optical fibers through a corresponding lens to a correspondingvertical-coupling element.

Embodiment 17: The method of embodiment 16 wherein the opticalsubassembly comprises a beam displacer, and the active alignment processcomprises projecting light from the array of optical fibers through thefirst lens array and the beam displacer to the at least onevertical-coupling element.

Embodiment 18: The method of embodiment 17 wherein the opticalsubassembly comprises a second lens array, and the active alignmentprocess comprises projecting light from the array of optical fibersthrough the first lens array, the beam displacer, and the second lensarray to the at least one vertical-coupling element.

Embodiment 19: The method of embodiment 18 wherein the opticalsubassembly comprises a half wave plate, and the active alignmentprocess comprises projecting light from the array of optical fibersthrough the first lens array, the beam displacer, the half wave plate,and the second lens array to the at least one vertical-coupling element.

Embodiment 20: The method of any of embodiments 1 to 19 wherein theactive alignment process comprises adjusting the position of the ferruleframe relative to the optical subassembly to maximize an overallefficiency of light transfer between the array of optical fibers and thephotonic integrated circuit.

Embodiment 21: The method of any of embodiments 1 to 20 wherein theferrule frame comprises at least one of glass, metal, or plastic.

Embodiment 22: The method of any of embodiments 1 to 20 wherein theferrule frame comprises a material that is transparent orsemi-transparent to ultra-violet (UV) light, and securely connecting theferrule frame to the optical subassembly comprises attaching the ferruleframe to the optical subassembly using an UV-curing adhesive.

Embodiment 23: The method of any of embodiments 1 to 22 whereinadjusting the position of the ferrule frame relative to the opticalsubassembly comprises adjusting the position of the ferrule frame alonga plane substantially parallel to the main surface of the photonicintegrated circuit.

Embodiment 24: The method of embodiment 23 wherein adjusting theposition of the ferrule frame along the plane substantially parallel tothe main surface of the photonic integrated circuit comprises at leastone of (i) adjusting the position of the ferrule frame along an x-axisrelative to the main surface of the photonic integrated circuit, (ii)adjusting the position of the ferrule frame along a y-axis relative tothe main surface of the photonic integrated circuit, or (iii) rotatingthe ferrule frame about a z-axis relative to the main surface of thephotonic integrated circuit;

-   -   wherein the x- and y-axes are substantially parallel to the main        surface of the photonic integrated circuit, and the z-axis is        substantially perpendicular to the main surface of the photonic        integrated circuit.

Embodiment 25: The method of any of embodiments 1 to 24 whereinadjusting the position of the ferrule frame relative to the opticalsubassembly comprises adjusting a distance of an end of the fiberconnector relative to the optical subassembly.

Embodiment 26: The method of any of embodiments 1 to 25 whereinadjusting the position of the ferrule frame relative to the opticalsubassembly comprises adjusting a tilt angle of an end surface of thefiber connector relative to the optical subassembly.

Embodiment 27: The method of any of embodiments 1 to 26 wherein aligningthe ferrule frame to the optical subassembly comprises aligning theferrule frame to the optical subassembly with a precision of at least 10μm accuracy.

Embodiment 28: The method of embodiment 27 wherein aligning the ferruleframe to the optical subassembly comprises aligning the ferrule frame tothe optical subassembly with a precision of at least 1 μm accuracy.

Embodiment 29: The method of embodiment 28 wherein aligning the ferruleframe to the optical subassembly comprises aligning the ferrule frame tothe optical subassembly with a precision of at least 0.1 μm accuracy.

Embodiment 30: The method of any of embodiments 1 to 29, wherein each ofthe vertical-coupling elements comprises at least one of asingle-polarization vertical grating coupler, a turning mirror, apolarization-diversity vertical grating coupler, a vertical cavitysurface emitting laser, a surface-normal modulator, or a photodiode.

Embodiment 31: The method of any of embodiments 1 to 15 and 20 to 30wherein the beam displacer comprises a polarization-dependent opticalelement.

Embodiment 32: An apparatus comprising:

-   -   a photonic integrated circuit including a plurality of        vertical-coupling elements disposed along a main surface of the        photonic integrated circuit;    -   an optical subassembly attached to the photonic integrated        circuit;    -   a ferrule frame that is configured to enable a fiber connector        to be removably connected to the ferrule frame and aligned with        the optical subassembly;    -   wherein the fiber connector is connected to an array of optical        fibers, and the optical subassembly is configured to transfer        light between the array optical fibers and the vertical-coupling        elements on the photonic integrated circuit;    -   wherein the ferrule frame is aligned to the optical subassembly        using an active alignment process in which light is transferred        between at least one optical fiber in the array of optical        fibers and the photonic integrated circuit through the optical        subassembly and at least one of the vertical-coupling elements,        and a position of the ferrule frame relative to the optical        subassembly is adjusted based on at least one characteristic of        the light transferred between the at least one optical fiber and        the photonic integrated circuit; and    -   wherein the ferrule frame is securely connected to the optical        subassembly after the active alignment process.

Embodiment 33: The apparatus of embodiment 32 wherein the ferrule frameenables the array of optical fibers to be aligned with the opticalsubassembly with a precision of at least 10 μm.

Embodiment 34: The apparatus of embodiment 32 wherein the ferrule frameenables the array of optical fibers to be aligned with the opticalsubassembly with a precision of at least 1 μm.

Embodiment 35: The apparatus of embodiment 32 wherein the ferrule frameenables the array of optical fibers to be aligned with the opticalsubassembly with a precision of at least 0.1 μm.

Embodiment 36: The apparatus of any of embodiments 32 to 35 wherein theoptical subassembly comprises a first lens array, and the ferrule moduleis configured to align the array of optical fibers with the lens array.

Embodiment 37: The apparatus of embodiment 36 wherein the opticalsubassembly comprises a beam displacer attached to the first lens array.

Embodiment 38: The apparatus of embodiment 37 wherein the opticalsubassembly comprises a second lens array, the beam displacer ispositioned between the first lens array and the second lens array, andthe second lens array is positioned between the beam displacer and thevertical-coupling elements.

Embodiment 39: The apparatus of embodiment 38 wherein the opticalsubassembly comprises a half wave plate positioned between the beamdisplacer and the second lens array.

Embodiment 40: The apparatus of embodiment 38 wherein the opticalsubassembly comprises a birefringent plate having holes, and thebirefringent plate is positioned between the beam displacer and thesecond lens array.

Embodiment 41: The apparatus of any of embodiments 32 to 35 wherein thefiber connector comprises a first lens array, and the ferrule module isconfigured to align the first lens array with the optical subassembly.

Embodiment 42: The apparatus of embodiment 41 wherein the opticalsubassembly comprises a beam displacer.

Embodiment 43: The apparatus of embodiment 42 wherein the opticalsubassembly comprises a second lens array positioned between the beamdisplacer and the vertical-coupling elements.

Embodiment 44: The apparatus of embodiment 43 wherein the opticalsubassembly comprises a half wave plate positioned between the beamdisplacer and the second lens array.

Embodiment 45: The apparatus of embodiment 43 wherein the opticalsubassembly comprises a birefringent plate having holes, and thebirefringent plate is positioned between the beam displacer and thesecond lens array.

Embodiment 46: The apparatus of any of embodiments 32 to 35, whereineach optical fiber comprises one or more fiber cores, the opticalsubassembly comprises at least one lens configured to communicate lightwith a single one of the fiber cores and a single one of thevertical-coupling elements.

Embodiment 47: The apparatus of any of embodiments 32 to 35, whereineach optical fiber comprises one or more fiber cores, the opticalsubassembly comprises a plurality of optical waveguides, each opticalwaveguide optically connecting a respective one of the fiber cores and arespective one of the vertical-coupling elements.

Embodiment 48: The apparatus of embodiment 47, wherein at least some ofthe optical waveguides are tapered.

Embodiment 49: The apparatus of any of embodiments 32 to 48, wherein theoptical subassembly comprises one or more polarization beam splitters.

Embodiment 50: The apparatus of any of embodiments 32 to 49, wherein theoptical subassembly comprises one or more polarization-rotatingelements.

Embodiment 51: The apparatus of any of embodiments 32 to 35, whereineach optical fiber comprises one or more fiber cores, the opticalsubassembly is configured to communicate light between a first number ofthe fiber cores and a second number of the vertical-coupling elements,and the second number is greater than the first number.

Embodiment 52: The apparatus of any of embodiments 32 to 51, whereineach of the vertical-coupling elements comprises at least one of asingle-polarization vertical grating coupler, a turning mirror, apolarization-diversity vertical grating coupler, a vertical cavitysurface emitting laser, a surface-normal modulator, or a photodiode.

Embodiment 53: The apparatus of any of embodiments 32 to 52 wherein theferrule frame comprises at least one of glass, metal, or plastic.

Embodiment 54: The apparatus of any of embodiments 32 to 52 wherein theferrule frame comprises a material that is transparent orsemi-transparent to ultra-violet (UV) light, and an UV-curing adhesiveis used to securely attach the ferrule frame to the optical subassembly.

Embodiment 55: The apparatus of any of embodiments 37 to 40 and 42 to 45wherein the beam displacer comprises a polarization-dependent opticalelement.

What is claimed is:
 1. An apparatus comprising: one or more opticalfibers having a plurality of fiber cores; a photonic integrated circuitincluding a plurality of vertical-coupling elements disposed along amain surface of the photonic integrated circuit; and a fiber-opticconnector connected between the one or more optical fibers and thephotonic integrated circuit to communicate light between the one or moreoptical fibers and the photonic integrated circuit, wherein thefiber-optic connector comprises a polarization beam splitter and apatterned birefringent plate; wherein the polarization beam splitter isconfigured to split an incident light beam from a corresponding fibercore into a first beam having a first polarization and a second beamhaving a second polarization different from the first polarization;wherein the patterned birefringent plate comprises a first region and asecond region, the first region has a first optical birefringence, thesecond region has a second optical birefringence that is different fromthe first optical birefringence, the first region is produced byapplying localized heating to a portion of a birefringent plate toreduce the birefringence at the first region, the second region is notsubject to the localized heating and retains its original birefringence;wherein the polarization beam splitter is configured to direct the firstbeam towards the first region and direct the second beam towards thesecond region; wherein the first region is configured to rotate thepolarization of the first beam by a first amount, the second region isconfigured to rotate the polarization of the second beam by a secondamount that is different from the first amount, the first and secondamounts are selected to cause the first and second beams to havesubstantially parallel polarization after passing the patternedbirefringent plate.
 2. The apparatus of claim 1 in which the patternedbirefringent plate is made from a single piece of birefringent material.3. The apparatus of claim 1 in which the first region is an integralportion of the patterned birefringent plate, and no glue or adhesive isused to bond the first region to other portions of the patternedbirefringent plate.
 4. The apparatus of claim 1 in which the patternedbirefringent plate has a top surface and a bottom surface, and the firstregion extends from the top surface to the bottom surface.
 5. Theapparatus of claim 1 in which the patterned birefringent plate has a topsurface and a bottom surface, the first region is positioned within thebirefringent plate at a first distance from the top surface and a seconddistance from the bottom surface.
 6. The apparatus of claim 1 in whichthe patterned birefringent plate has a top surface and a bottom surface,the first region extends from the top surface to a location within thebirefringent plate at a distance from the bottom surface.
 7. Theapparatus of claim 1 in which the polarization beam splitter isconfigured to cause the second polarization of the second beam to beorthogonal to the first polarization of the first beam after the firstand second beams exit the polarization beam splitter; wherein the firstregion has substantially zero birefringence, and the second region isconfigured to rotate the polarization of the second beam by about90°+n×180°, 0≤n, n being an integer.
 8. The apparatus of claim 1 inwhich the one or more optical fibers comprise an array of at least 2rows and at least 8 columns of fiber cores; wherein the patternedbirefringent plate comprises at least two first regions, each firstregion has an elongated shape that extends along a direction parallel tothe row direction; wherein the second region comprises the birefringentmaterial adjacent to the first regions; wherein the polarization beamsplitter is configured to split 8 incident light beams from 8corresponding fiber cores of a row into 8 first beams having the firstpolarization and 8 second beams having the second polarization, directthe 8 first beams toward a first region, and direct the 8 second beamsto the second region; wherein upon the 8 first beams passing through thefirst region and the 8 second beams passing through the second region,the 8 first beams and the 8 second beams have substantially parallelpolarization.
 9. The apparatus of claim 1 in which the one or moreoptical fibers comprise an array of at least 2 rows and at least 8columns of fiber cores; wherein the patterned birefringent platecomprises an array of at least 2 rows and at least 8 columns of firstregions; wherein the second region comprises the birefringent materialadjacent to the first regions; wherein the polarization beam splitter isconfigured to split 8 incident light beams from 8 corresponding fibercores of a row into 8 first beams having the first polarization and 8second beams having the second polarization different from the firstpolarization, direct the 8 first beams toward 8 corresponding firstregions, and direct the 8 second beams towards the second region;wherein upon the 8 first beams passing through the 8 first regions andthe 8 second beams passing through the second region, the 8 first beamsand the 8 second beams have substantially parallel polarization.
 10. Theapparatus of claim 1 in which the fiber-optic connector comprises afirst connector part and a second connector part, the first connectorpart is removably coupled to the second connector part, the firstconnector part is optically coupled to the plurality of fiber cores, thesecond connector part is optically coupled to the plurality ofvertical-coupling elements, and both the polarization beam splitter andthe patterned birefringent plate are included in the first connectorpart.
 11. The apparatus of claim 1 in which the fiber-optic connectorcomprises a first connector part and a second connector part, the firstconnector part is removably coupled to the second connector part, thefirst connector part is optically coupled to the plurality of fibercores, the second connector part is optically coupled to the pluralityof vertical-coupling elements, and both the polarization beam splitterand the patterned birefringent plate are included in the secondconnector part.
 12. The apparatus of claim 1 in which the fiber-opticconnector comprises a first connector part and a second connector part,the first connector part is removably coupled to the second connectorpart, the first connector part is optically coupled to the plurality offiber cores, the second connector part is optically coupled to theplurality of vertical-coupling elements, the polarization beam splitteris included in the first connector part, and the patterned birefringentplate is included in the second connector part.
 13. An apparatuscomprising: a first connector part that is part of a fiber-opticconnector configured to be connected between one or more optical fibershaving a plurality of fiber cores and a photonic integrated circuitincluding a plurality of vertical-coupling elements disposed along amain surface of the photonic integrated circuit, wherein the fiber-opticconnector comprises a polarization beam splitter, and the firstconnector part comprises a patterned birefringent plate; wherein thepolarization beam splitter is configured to split an incident light beamfrom a corresponding fiber core into a first beam having a firstpolarization and a second beam having a second polarization differentfrom the first polarization; wherein the patterned birefringent platecomprises non-uniform birefringence produced by applying localizedheating to the birefringent plate to cause one or more regions of thebirefringent plate to have reduced birefringence as compared to one ormore other regions of the birefringent plate, resulting in at least onelower-birefringence region and at least one higher-birefringence regionin the patterned birefringent plate; wherein the polarization beamsplitter is configured to direct the first beam towards alower-birefringence region in the patterned birefringent plate anddirect the second beam towards a higher-birefringence region in thepatterned birefringent plate; wherein the lower-birefringent region isconfigured to rotate the polarization of the first beam by a firstamount, the higher-birefringent region is configured to rotate thepolarization of the second beam by a second amount that is differentfrom the first amount, the first and second amounts are selected tocause the first and second beams to have substantially parallelpolarization after passing the patterned birefringent plate.
 14. Theapparatus of claim 13 in which the lower-birefringence region hassubstantially zero birefringence.
 15. The apparatus of claim 13 in whichthe first connector part comprises the polarization beam splitter. 16.The apparatus of claim 13 in which the lower-birefringence region is anintegral portion of the patterned birefringent plate, and no glue oradhesive is used to bond the lower-birefringence region to otherportions of the patterned birefringent plate.
 17. A method offabricating a fiber-optic connector, the method comprising: applyinglocalized heating to a birefringent plate to produce a patternedbirefringent plate, in which the localized heating modifiesbirefringence of a plurality of first regions in the birefringent plateto cause the first regions to have birefringence that is different fromthe birefringence of second regions that do not receive the localizedheating; and attaching the patterned birefringent plate to a secondcomponent to form a fiber-optic connector that is configured to becoupled to at least one of a plurality of optical fibers or a pluralityof coupling elements on a photonic integrated circuit.
 18. The method ofclaim 17 in which the localized heating causes the first regions to havereduced birefringence.
 19. The method of claim 17 in which the localizedheating causes the first regions to have substantially zerobirefringence.
 20. The method of claim 17 in which applying localizedheating comprises applying a laser beam to the first regions to locallyheat the first regions.
 21. The method of claim 17 in which the firstregions comprise elongated strips, the elongated strips have lengthwisedirections that are parallel to one another, and the strips are spacedapart in a direction perpendicular to the lengthwise direction.
 22. Themethod of claim 17 in which the patterned birefringent plate comprisesan array of at least 2 rows and at least 8 columns of first regions. 23.The method of claim 17 in which prior to applying the localized heating,the birefringent plate comprises a crystalline quartz plate havingpredefined birefringence, and the localized heating produces amorphousfused silica having modified, lower, or substantially no birefringencein the first regions.
 24. The method of claim 17 in which applyinglocalized heating comprises sequentially applying localized heating tothe first regions one after another.
 25. The method of claim 17 in whichapplying localized heating comprises applying localized heating tomultiple first regions in parallel.
 26. The method of claim 17 in whichthe birefringent plate is configured to modify a polarization state of afirst set of light beams that pass through the first regions of thebirefringent plate relative to a polarization state of a second set oflight beams that pass through the second regions of the birefringentplate.
 27. The method of claim 17 in which applying localized heating tothe birefringent plate comprises applying localized heating to thebirefringent plate to modify birefringence of a two-dimensional array offirst regions in the birefringent plate to cause the array of firstregions to have birefringence that is different from the birefringenceof second regions that do not receive the localized heating, and thetwo-dimensional array comprises at least 2 rows and at least 8 columns.28. The method of claim 27 in which the spacing between two adjacentrows in the two-dimensional array is identical to the spacing betweentwo adjacent columns in the two-dimensional array.
 29. The method ofclaim 27 in which the fiber-optic connector is configured to beoptically coupled to a two-dimensional array of optical fibers.
 30. Themethod of claim 29 in which the fiber-optic connector is configured toenable a first set of light beams and a second set of light beams to betransmitted between the two-dimensional array of optical fibers and atwo-dimensional array of vertical coupling elements, and thebirefringent plate is configured to modify a polarization state of thefirst set of light beams that pass through the first regions of thebirefringent plate relative to a polarization state of the second set oflight beams that pass through the second regions of the birefringentplate.
 31. The method of claim 27 in which the fiber-optic connector isconfigured to be optically coupled to a two-dimensional array ofvertical coupling elements on the photonic integrated circuit.
 32. Themethod of claim 31 in which the fiber-optic connector is configured toenable a first set of light beams and a second set of light beams to betransmitted between a two-dimensional array of optical fibers and thetwo-dimensional array of vertical coupling elements, and thebirefringent plate is configured to modify a polarization state of thefirst set of light beams that pass through the first regions of thebirefringent plate relative to a polarization state of the second set oflight beams that pass through the second regions of the birefringentplate.
 33. The method of claim 27 in which each of at least some of thefirst regions has a substantially circular, oval, triangular, square, orrectangular shape.
 34. The method of claim 27 in which thetwo-dimensional array of first regions comprise at least 2 parallelstrips, and applying localized heating to the birefringent platecomprises applying localized heating to modify birefringence of the atleast 2 parallel strips in the birefringent plate to cause the at least2 parallel strips to have birefringence that is different from thebirefringence of the second regions that do not receive the localizedheating.
 35. The method of claim 34 in which each strip has a width in arange from 50 μm to 1000 μm.
 36. The method of claim 35 in which eachstrip has a width in a range from 100 μm to 600 μm.
 37. The method ofclaim 36 in which each strip has a width in a range from 200 μm to 400μm.
 38. The method of claim 17 in which the fiber-optic connector isconfigured to be optically coupled to a plurality of vertical couplingelements on the photonic integrated circuit, and the fiber-opticconnector is configured to enable the first set of light beams and thesecond set of light beams to be transmitted between the plurality ofoptical fibers and the plurality of vertical coupling elements.
 39. Themethod of claim 38 in which applying the localized heating to thebirefringent plate comprises applying the localized heating to thebirefringent plate to reduce the birefringence at the first regions. 40.The method of claim 39 in which applying the localized heating to thebirefringent plate comprises applying the localized heating to thebirefringent plate to reduce the birefringence at the first regions tosubstantially zero birefringence.
 41. The method of claim 39 in whichapplying the localized heating to the birefringent plate comprisesapplying the localized heating to the birefringent plate to reduce thebirefringence at the first regions such that the second set of lightbeams that pass through the second regions have polarization that isrotated about 90°+n×180°, 0≤n, n being an integer, relative topolarization of the first set of light beams that pass through the firstregions.
 42. The method of claim 39 in which the first optical connectorpart comprises a walk-off element configured to: receive a plurality oflight beams from the plurality of optical fibers, split the light beamsinto first beam components and second beam components, the second beamcomponents have polarization that is orthogonal to the polarization ofthe first beam components, direct the first beam components toward thefirst regions having lower birefringence, and direct the second beamcomponents toward the second regions having higher birefringence. 43.The method of claim 42 in which applying the localized heating to thebirefringent plate comprises applying the localized heating to thebirefringent plate to reduce the birefringence at the first regions suchthat the second set of light beams that pass through the second regionshave polarization that is rotated about 90°+n×180°, 0≤n, n being aninteger, relative to polarization of the first set of light beams thatpass through the first regions, wherein the walk-off element isconfigured such that upon exiting the walk-off element the first beamcomponents have first polarization, and the second beam components havesecond polarization that is substantially orthogonal to the firstpolarization, wherein the first and second regions of the birefringentplate are configured such that after passing the first and secondregions the first beam components have polarization that issubstantially parallel to the polarization of the second beamcomponents.
 44. The method of claim 42 in which the walk-off elementseparates the first beam component and the second beam component along awalk-off direction, each of at least some of the first regions has adimension measured along a direction parallel to the walk-off directionin a range from 50 μm to 1000 μm.
 45. The method of claim 44 in whicheach of at least some of the first regions has a dimension measuredalong a direction parallel to the walk-off direction in a range from 100μm to 600 μm.
 46. The method of claim 45 in which each of at least someof the first regions has a dimension measured along a direction parallelto the walk-off direction in a range from 200 μm to 400 μm.
 47. Themethod of claim 17 in which applying localized heating to thebirefringent plate comprises applying localized heating to thebirefringent plate to modify birefringence of the two-dimensionalpattern of first regions in the birefringent plate such that thebirefringent plate is configured to modify polarization of light passingthe birefringent plate in a way that is equivalent to modification ofpolarization of light passing a half-wave plate having openings at thetwo-dimensional pattern of first regions.
 48. The method of claim 17 inwhich the birefringent plate comprises a first surface and a secondsurface, wherein applying localized heating to the birefringent platecomprises applying localized heating to first regions that extend fromthe first surface to the second surface.
 49. The method of claim 17 inwhich the birefringent plate comprises a first surface and a secondsurface, wherein applying localized heating to the birefringent platecomprises applying localized heating to first regions that arepositioned within the birefringent plate and spaced at a first distancefrom the first surface and a second distance from the second surface.50. The method of claim 17 in which the birefringent plate comprises afirst surface and a second surface, the first surface is closer to theplurality of optical fibers relative to the second surface, whereinapplying localized heating to the birefringent plate comprises applyinglocalized heating to first regions that extend from the first surface toa location inside the birefringent plate, the first regions are spacedat a distance from the second surface.
 51. The method of claim 17 inwhich the birefringent plate comprises a first surface and a secondsurface, the first surface is closer to the plurality of couplingelements relative to the second surface, wherein applying localizedheating to the birefringent plate comprises applying localized heatingto first regions that extend from the second surface to a locationinside the birefringent plate, the first regions are spaced at adistance from the first surface.
 52. The method of claim 17 in whichapplying localized heating comprises using one or more laser beams toapply the localized heating.